DOCSLIB.ORG

Notices of the American Mathematical Society

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Calendar This Calendar lists all of the meetings which have been approved by the Council up to the date this issue of the cJ{oliiriJ was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Abstracts should be submitted on special forms which are available in most departments of mathematics; forms can also be obtained by writing to the headquarters of the Society. Abstracts to be presented at the meeting in person must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline for the meeting. Meeting Deadline for Abstracts* Number Date Place and News Items 716 October 26, 1974 Middletown, Connecticut Sept. 3, 1974 717 November 8-9, 1974 Nashville, Tennessee Sept, 25, 1974 718 November 23, 1974 Los Angeles, California Sept. 25, 1974 719 November 23, 1974 Houston, Texas Sept. 25, 1974 720 January 23-27, 1975 Washington, D. C. Nov, 6, 1974 (81st Annual Meeting) March 20-21, 1975 Mobile, Alabama March 23-26, 1975 New York, New York April 18-19, 1975 Monterey, California August 18-22, 1975 Kalamazoo, Michigan November 7-8, 1975 Blacksburg, Virginia November 15, 1975 Los Angeles, California January 22-26, 1976 San Antonio, Texas (82nd Annual Meeting) *Deadline for abstracts not presented at a meeting (by title). October 1974 issue: August 29 OTHER EVENTS January 1975 Symposium on Some Mathematical Questions in Biology New York, New York November 6, 1974 January 1975 Symposium on Theory vs. Practice in the Finite Element Method - New York, New York The zip code of the Post Office Box of the Society has been changed from 02904 to 02940, Correspondents are requested to note this change in their records, PI.. affix the peel-ofF label on th- cNOiu:aJ to correspondence with the Society concerning fiscal matters, changes of address, promotioDa, or when placing orders for books and joumals. The ci-/diaiJ of the American Mathematical Society is published by the American Mathematical Society, P. 0. Box 6248, Providence, Rhode laland 02940, in January, February, April, June, Augult, October, November, and December. Subscription per annual volume is $10. Member subscription of $5 is included in annual dues. Price per copy $3. Special price for copiell aold at rqistration dab of meetinga of the Society, $1 per copy. Subscriptions, orders for back numbers (back issu011 of the last two yean only are available), and inquiries should be addreeeed to the American Mathematical Society, P. 0. Box 6248, Providence, Rhode Ialand 02940. Second clau postage paid at Providence, Rhode Ialand, and additional mailing offices. Copyright © 197 4 by tbe American Mathematical Society Printed io tbe United Statea of Amema OF THE AMERICAN MATHEMATICAL SOCIETY Everett Pitcher and Gordon L. Walker, Editors Wendell H. Fleming, Associate Editor CONTENTS CALENDAR OF MEETINGS . Inside Front Cover PRELIMINARY ANNOUNCEMENTS OF MEETINGS 194 CHAIRMEN AND TOPICS OF SPECIAL SESSIONS 196 INVITED SPEAKERS AT AMS MEETINGS 197 SYMPOSIUM ON SOME MATHEMATICAL QUESTIONS IN BIOLOGY 198 INTERNATIONAL CONGRESS OF MATHEMATICIANS 199 NOMINATIONS FOR VICE-PRESIDENT OR MEMBER-AT-LARGE 204 NONACADEMIC EMPLOYMENT OF PH. D. •S ......... 206 DOCTORAL SCIENTISTS AND ENGINEERS IN THE UNITED STATES 212 ACKNOWLEDGEMENTS . • . • . 215 SPECIAL MEETINGS INFORMATION CENTER 218 QUERIES ..•..•.. 220 LETTERS TO THE EDITOR . 222 NEW AMS PUBLICATIONS . 224 PERSONAL ITEMS . 230 NEWS ITEMS AND ANNOUNCEMENTS 198, 211, 219, 221, 223, 231 ERRATA TO ABSTRACTS 234 ABSTRACTS ..... A-473 SITUATIONS WANTED . A-511 PRELIMINARY ANNOUNCEMENTS OF MEETINGS The Seven Hundred Sixteenth Meeting Wesleyan University Middletown, Connecticut October 26, 1974 The seven hundred sixteenth meeting of the Balcony Suite $35 (2-6) (2 dble beds & American Mathematical Society will be held at 1 sofa bed) Wesleyan University, Middletown, Connecticut, Each additional person $3. OO.Cots, $3. 00. on Saturday, October 26, 1974. Plus 6% Connecticut sales tax. By invitation of the Committee to Select Hour Speakers for Eastern Sectional Meetings, MIDDLETOWN MOTOR INN (1 mi) there will be two one-hour addresses. Professor Washington Street Extension (Meriden Road, Philip J. Davis of Brown University will speak Route 66) on "Geometry, computer graphics, and theorems Middletown, CT 06457 of visual type". Professor Mark Kac of Rocke­ Phone: (203) 346-9251 feller University will speak on "Some analytic Single $11-12 problems suggested by statistical mechanics". Double $13-14 (1 bed) Professor Ernest G. Manes of the Uni­ Twin $16-17 (2 beds) versity of Massachusetts, Amherst, will organ­ Each additional person, $2. 00 ize a special session on Category Theory as Plus 6% Connecticut sales tax Applied to Analysis and Topology. Sessions for contributed ten-minute papers Reservations should be made directly with will be scheduled in the morning and the after­ the motel, mention of this meeting being made in noon. No provision will be made for late papers. the correspondence or call. All prices quoted in Abstracts should be submitted to the American this announcement are as of June 1974. Mathematical Society, P.o. Box 6248, Provi­ dence, Rhode Island 02940, so as to arrive prior TRAVEL to the deadline of September 3, 1974. See page 179 of the June 1974 c}(otiui) for new format Middletown, located in central Connecticut on the Connecticut required for abstracts. The final pro~:r:;am will River, is approximately 15 appear in the October issue of these cJIIotiui), miles south of Hartford and 25 miles northeast of New Haven. Midway between New York City ACCOMMODATIONS and Boston, it is about 2-1/4 hours of driving time from the center of each city. State Highways The following motels provide the accom­ 9, 17, and 66 pass thru Middletown, and National modations nearest to the Wesleyan University Interstate Highway I-91 is 5 to 8 miles away. campus, distance in miles being given next to Middletown is served by Continental Trailways the name: and Greyhound Bus Lines. Bradley International Airport, about 32 miles north of Middletown, is CRESTLINE MOTEL (1-1/2 mi) off I-91 in Windsor Locks, and Tweed-New Haven Meriden Road (Route 66) Airport is just outside of New Haven. Direct taxi Middletown, CT 06457 fare between these airports and Middletown is Phone: (203) 347-6955 around $20. The nearest Penn Central passenger Single $10.60 train station (Amtrak) is located in Meriden, Double $12.75 (1 bed) about 10 miles west of Middletown. The taxi Twin $14.85 (2 beds) fare between Meriden and Middletown is approx­ Quadruple $19.10 (2 beds) imately $9. Scheduled limousine service between 6% Connecticut sales tax included Bradley International Airport and Lord Cromwell Motor Inn (see under ACCOMMODATIONS above) LORD CROMWELL MOTOR INN (3 mi) is available at $6. 50 one way and $11. 50 round Berlin Road (Route 72) trip; for information on schedules and fares, Cromwell, CT 06416 contact Central Connecticut Limousine Service, Phone: (203) 347-7427 Inc., 65 Quinnipiac Avenue, North Haven, CT (Numbers in parentheses refer to number of 06473, telephone: (203) 562-3165. persons.) Single $16 (1) $20 (2) (1 dble bed) Walter H. Gottschalk Double $18 (1) $25 (2) (2 dble beds) Associate Secretary King $18 (1) $25 (2) (1 king bed) Middletown, Connecticut 194 The Seven Hundred Seventeenth Meeting Vanderbilt U Diversity Nashville, Tennessee November 8-9,1974 The seven hundred seventeenth meeting of Three cafeterias on campus will be open the American Mathematical Society will be held for all meals. Also a list of local restaurants at Vanderbilt University in Nashville, Tennessee, will be available at the registration desk. on Friday and Saturday, November 8-9, 1974. Three motels near the campus are holding By invitation of the Committee to Select blocks of rooms with a reservation deadline of Hour Speakers for Southeastern Sectional Meet­ October 25. Reservations should be made direct­ ings, there will be three one-hour addresses, ly with them, with mention of this meeting in­ the first being at 1:00 p.m. on Friday in the au­ cluded in that correspondenceo The zip code for ditorium of the Sarratt Commons. All other ses­ each of the following is 37203. sions will be held in the Stevenson Center for the Natural Sciences. Professor Trevor Evans of HOLIDAY INN-VANDERBILT Emory University will give an address entitled (100 rooms reserved) "Word problems". An address entitled "Geom­ 2613 West End Avenue etry of sub-manifolds in Euclidean space" will (five blocks from the Stevenson Center) be given by Professor Robert B. Gardner of the Phone: (615) 383-1147 University of North Carolina, and Professor Single $14. 00 up James R. Retherford of Louisiana State Univer­ Double $18. 50 up (one bed) sity will present an address entitled "Banach TWins $20.50 up (two beds) ideals of operators". There will be three special sessions in ALLEN MOTEL addition to the regular sessions. Professor J. v. (15 rooms reserved) Brawley of Clemson University, Clemson, South 2004 West End Avenue Carolina is arranging a special session on Enu­ (six blocks from the Stevenson Center) merative Combinatorial Theory, Professor Phone: (615) 327-1841 Robert M. McConnel of the University of Ten­ Single $12.00 nessee, Knoxville, Tennessee is arranging a Double $14.00 special session on Number Theory, and Pro­ fessor Richard S. Varga of Kent State Univer­ sity, Kent, Ohio is organizing a special session ANCHOR MOTEL on Approximation Theory. Any member of AMS (40 rooms reserved) who would like to have his or her paper consid­ 1921 West End Avenue ered for inclusion in one of the special sessions (six blocks from the Stevenson Center) Phone: (615) should have his or her abstract so marked and in 327-4581 Providence at least two weeks before the regular Single $13.
Recommended publications
  • Reflections on a Career in Mathematics Masamichi Takesaki

    Reflections on a Career in Mathematics Masamichi Takesaki

    Reflections on a career in Mathematics Masamichi Takesaki Professor of Mathematics, Emeritus, Department of Mathematics, UCLA Los Angeles, California, USA My Personal History As erroneous information about my career has been posted on the internet, I will begin by correcting the record. ⦁ 1956, Spring: Graduated from Mathematical Institute, Tohoku University, earning a Bachelor’s Degree. ⦁ 1956-1958: Master’s Degree Student at Mathematical Institute, Tohoku University, earning a Master’s Degree in Mathematics. ⦁ 1958, April through June: Ph D Student at Mathematical Institute, Tohoku University, withdrawing from the Ph D course in order to take a position at the Tokyo Institute Technology. ⦁ 1958, July through 1963, June: Research Assistant at Department of Mathematics, Tokyo Institute of Technology. ⦁ 1963, July through 1970 June 30: Associate Professor of Mathematics, Mathematical Institute, Tohoku University. ⦁ 1965, May: PhD of Mathematics granted from Tohoku University. ⦁ 1968 September 1- 1969, June 30: Visiting Associate Professor, Department of Mathematics, University of Pennsylvania. ⦁ 1969, July 1 - 1970, to June 30: Visiting Associate Professor, Department of Mathematics, UCLA. Leave of Absence from Tohoku University for 1968 - 1970. ⦁ 1970, July 1 through 2004, June 30: Professor of Mathematics, Department of Mathematics, UCLA. ⦁ 2004 July – present: Professor of Mathematics, Emeritus, Department of Mathematics, UCLA. ⦁ Various Visiting Positions throughout my career at UCLA. Introduction I would like to talk about my experiences as an operator algebraist and make some observations based on those experiences. The period 1956 through 1958, when I was working toward my Master’s degree, marked a quiet but very significant decision in the US science program, the importance of which was not widely recognized in Japan.
  • Modulation Spaces, Wiener Amalgam Spaces, and Brownian Motions

    Modulation Spaces, Wiener Amalgam Spaces, and Brownian Motions

    MODULATION SPACES, WIENER AMALGAM SPACES, AND BROWNIAN MOTIONS ARP´ AD´ BENYI´ AND TADAHIRO OH Abstract. We study the local-in-time regularity of the Brownian motion with respect p;q p;q to localized variants of modulation spaces Ms and Wiener amalgam spaces Ws . We p;q p;q show that the periodic Brownian motion belongs locally in time to Ms (T) and Ws (T) for (s − 1)q < −1, and the condition on the indices is optimal. Moreover, with the p;q p;q Wiener measure µ on T, we show that (Ms (T); µ) and (Ws (T); µ) form abstract Wiener spaces for the same range of indices, yielding large deviation estimates. We also establish the endpoint regularity of the periodic Brownian motion with respect to a Besov-type s s space bp;1(T). Specifically, we prove that the Brownian motion belongs to bp;1(T) for (s − 1)p = −1, and it obeys a large deviation estimate. Finally, we revisit the regularity s of Brownian motion on usual local Besov spaces Bp;q, and indicate the endpoint large deviation estimates. Contents 1. Introduction 1 1.1. Function spaces of time-frequency analysis 4 1.2. Brownian motion 6 2. Regularity of Brownian motion 7 2.1. Modulus of continuity 7 2.2. Fourier analytic representation 8 2.3. Alternate proof for the Besov spaces 12 3. Large deviation estimates 15 3.1. Abstract Wiener spaces and Fernique's theorem 15 s 3.2. Large deviation estimates for bp;1(T) at the endpoint (s − 1)p = −1 20 1 2 3.3.
  • FOURIER STANDARD SPACES and the Kernel Theorem

    FOURIER STANDARD SPACES and the Kernel Theorem

    Numerical Harmonic Analysis Group FOURIER STANDARD SPACES and the Kernel Theorem Hans G. Feichtinger [email protected] www.nuhag.eu . Currently Guest Prof. at TUM (with H. Boche) Garching, TUM, July 13th, 2017 Hans G. Feichtinger [email protected] www.nuhag.euFOURIER. Currently STANDARD GuestSPACES Prof. at TUM and the (with Kernel H. Boche) Theorem OVERVIEW d We will concentrate on the setting of the LCA group G = R , although all the results are valid in the setting of general locally compact Abelian groups as promoted by A. Weil. |||||||||||||||||||||- Classical Fourier Analysis pays a lot of attention to p d L (R ); k · kp because these spaces (specifically for p 2 f1; 2; 1g) are important to set up the Fourier transform as an integral transform which also respects convolution (we have the convolution theorem) and preserving the energy (meaning that it is 2 d a unitary transform of the Hilbert space L (R ); k · k2 ). |||||||||||||||||||||- d Occasionally the Schwartz space S(R ) is used and its dual 0 d S (R ), the space of tempered distributions (e.g. for PDE and d the kernel theorem, identifying operators from S(R ) to 0 d 0 2d S (R ) with their distributional kernels in S (R )). Hans G. Feichtinger FOURIER STANDARD SPACES and the Kernel Theorem OVERVIEW II S d In the last 2-3 decades the Segal algebra 0(R ); k · kS0 1 d (equal to the modulation space (M (R ); k · kM1 )) and its dual, 0 d 1 d S 0 M ( 0 (R ); k · kS0 ) or (R ) have gained importance for many questions of Gabor analysis or time-frequency analysis.
  • Completeness of Shifted Dilates in Invariant Banach Spaces of Tempered Distributions

    Completeness of Shifted Dilates in Invariant Banach Spaces of Tempered Distributions

    Completeness of shifted dilates in invariant Banach spaces of tempered distributions Hans G. Feichtinger∗ Anupam Gumber y August 17, 2020 Abstract We show that well-established methods from the theory of Banach modules and time-frequency analysis allow to derive completeness results for the collection of shifted and dilated version of a given (test) function in a quite general setting. While the basic ideas show strong similarity to the arguments used in a recent paper by V. Katsnelson we extend his results in several directions, both relaxing the assumptions and widening the range of applications. There is no need for the 2 Banach spaces considered to be embedded into L (R); k · k2 , nor is the Hilbert space structure relevant. We choose to present the results in the setting of the Euclidean spaces, because then the 0 d Schwartz space S (R )(d ≥ 1) of tempered distributions provides a well-established environment for mathematical analysis. We also establish connections to modulation spaces and Shubin classes d Qs(R ); k · kQs , showing that they are special cases of Katsnelson's setting (only) for s ≥ 0. Keywords: Beurling algebra, Shubin spaces, modulation spaces, approximation by translations, Banach spaces of tempered distributions, Banach modules, compactness 2010 Mathematics Subject Classification. Primary 43A15, 41A30, 43A10, 41A65, 46F05, 46B50; Secondary 43A25, 46H25, 46A40 1 Introduction The motivation for the present paper lies in the study of [24], which shows that the set of all shifted, di- lated Gaussians is total in certain translation and modulation invariant Hilbert spaces of functions which are 2 continuously embedded into L (R); k · k2 .
  • ABSTRACT XUE, XIANGZHONG. Electronic

    ABSTRACT XUE, XIANGZHONG. Electronic

    ABSTRACT XUE, XIANGZHONG. Electronic System Optimization Design via GP-Based Surrogate Modeling. (Under the direction of Dr. Paul D. Franzon.) For an electronic system with a given circuit topology, the designer’s goal is usually to automatically size the device and components to achieve globally optimal performance while at the same satisfying the predefined specifications. This goal is motivated by a human desire for optimality and perfection. This research project improves upon current optimization strategies. Many types of convex programs and convex fitting techniques are introduced and compared, and the evolution of Geometric Program (GP)-based optimization approaches is investigated through a literature review. By these means, it is shown that a monomial-based GP can achieve optimal performance and accuracy only for long-channel devices, and that a piecewise linear (PWL)-based GP works well only for short-channel, narrow devices without many data fitted. Based on known GP optimizer and convex PWL fitting techniques, an innovative surrogate modeling and optimization algorithm is proposed to further improve performance accuracy iteratively for a wide transistor with a short channel. The new surrogate strategy, which comprises a fine model and a coarse model, can automatically size the device to create a reusable system model for designing electronic systems and noticeably improving prediction accuracy, particularly when compared to the pure, GP-based optimization method. To verify the effectiveness and viability of the proposed surrogate strategy, a widely used two-stage optimization design is employed, entailing an operational amplifier (op-amp) and LC-tuned oscillator. In addition, an involved analysis and simulation demonstrate that the optimal results of both coarse and fine models in the proposed surrogate strategy may gradually converge to each other iteratively while achieving over 10% improvement in performance accuracy compared to the previous, PWL-based GP algorithm.
  • Mathematicalsciences News

    Mathematicalsciences News

    mathematical sciences news 2015 contents 2015 Letter from Department 03 Head, Tom Bohman Math News Shorts 04 Faculty Notes 06 Editor-in-Chief Tom Bohman Writer Feature 08 Amy Pavlak Laird Alumnus and Nobel Laureate Contributing Writers Bill Hrusa John Nash Wins Abel Prize David Kinderlehrer Dejan Slep ´cev Photography Democracy 2.1 16 Carnegie Mellon University photographers Ken Andreyo and Tim Kaulen Graphic Design Carnegie Mellon University Marketing & Communications Po-Shen Loh Receives 20 NSF CAREER Award Carnegie Mellon University Department of Mathematical Sciences Wean Hall 6113 Pittsburgh, PA 15213 Boris Bukh Wins Sloan 22 math.cmu.edu Research Fellowship Carnegie Mellon University does not discriminate in admission, employment, or administration of its programs or activities on the basis of race, color, national origin, sex, handicap or disability, age, sexual orientation, gender identity, religion, Undergraduate creed, ancestry, belief, veteran status or genetic 24 information. Furthermore, Carnegie Mellon University does not discriminate and is required Research not to discriminate in violation of federal, state or local laws or executive orders. Inquiries concerning the application of and compliance with this statement should be directed to the Vice President for Campus Affairs, Carnegie Mellon University, 5000 Forbes Avenue, Class of 2015 Pittsburgh, PA 15213, telephone 412-268-2056. 26 Obtain general information about Carnegie Mellon University by calling 412-268-2000. Produced for the Department of Mathematical Sciences by the Marketing & Communications, November, 2015, 16-177. ©2015 Carnegie Mellon University, All rights reserved. No part of this publication may be reproduced in any form without written permission from Carnegie Mellon Unversity’s Department of Mathematical Sciences.
  • Continuity and Schatten–Von Neumann Properties for Pseudo–Differential Operators and Toeplitz Operators on Modulation Spaces

    Continuity and Schatten–Von Neumann Properties for Pseudo–Differential Operators and Toeplitz Operators on Modulation Spaces

    The Erwin Schr¨odinger International Boltzmanngasse 9 ESI Institute for Mathematical Physics A-1090 Wien, Austria Continuity and Schatten–von Neumann Properties for Pseudo–Differential Operators and Toeplitz operators on Modulation Spaces Joachim Toft Vienna, Preprint ESI 1732 (2005) November 2, 2005 Supported by the Austrian Federal Ministry of Education, Science and Culture Available via http://www.esi.ac.at CONTINUITY AND SCHATTEN-VON NEUMANN PROPERTIES FOR PSEUDO-DIFFERENTIAL OPERATORS AND TOEPLITZ OPERATORS ON MODULATION SPACES JOACHIM TOFT p,q Abstract. Let M(ω) be the modulation space with parameters p,q and weight function ω. We prove that if p1 = p2, q1 = q2, α ∞ ω1 = ω0ω and ω2 = ω0, and ∂ a/ω0 ∈ L for all α, then the Ψdo p1,q1 p2,q2 p,q at(x, D) : M(ω1) → M(ω2 ) is continuous. If instead a ∈ M(ω) for appropriate p, q and ω, then we prove that the map here above is continuous, and if in addition pj = qj = 2, then we prove that at(x, D) is a Schatten-von Neumann operator of order p. We use these results to discuss continuity for Toeplitz operators. Mathematics Subject Classifications (2000): Primary: 47B10, 35S05, 47B35, 47B37; Secondary: 42B35, 46E35. Key words: Schatten-von Neumann, pseudo-differential operators, Toeplitz oper- ators, modulation spaces, embeddings. 0. Introduction In [G2] and [GH1], Gr¨ochenig and Heil present an alternative method, based on time-frequency analysis when investigating pseudo-differential operators with non-smooth symbols belonging to non-weighted modu- lation spaces. Here they make suitable Gabor expansions of the sym- bols, which in certain extent essentially reduce the problems in such way that the symbols are translations and modulations of a fix and well-known function.
  • Notices of the American Mathematical Society

    Notices of the American Mathematical Society

    OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 16, NUMBER 3 ISSUE NO. 113 APRIL, 1969 OF THE AMERICAN MATHEMATICAL SOCIETY Edited by Everett Pitcher and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings ..................................... 454 Program for the April Meeting in New York ..................... 455 Abstracts for the Meeting - Pages 500-531 Program for the April Meeting in Cincinnati, Ohio ................. 466 Abstracts for the Meeting -Pages 532-550 Program for the April Meeting in Santa Cruz . ......... 4 73 Abstracts for the Meeting- Pages 551-559 PRELIMINARY ANNOUNCEMENT OF MEETING ....................•.. 477 NATIONAL REGISTER REPORT .............. .. 478 SPECIAL REPORT ON THE BUSINESS MEETING AT THE ANNUAL MEETING IN NEW ORLEANS ............•................... 480 INTERNATIONAL CONGRESS OF MATHEMATICIANS ................... 482 LETTERS TO THE EDITOR ..................................... 483 APRIL MEETING IN THE WEST: Some Reactions of the Membership to the Change in Location ....................................... 485 PERSONAL ITEMS ........................................... 488 MEMORANDA TO MEMBERS Memoirs ............................................. 489 Seminar of Mathematical Problems in the Geographical Sciences ....... 489 ACTIVITIES OF OTHER ASSOCIATIONS . 490 SUMMER INSTITUTES AND GRADUATE COURSES ..................... 491 NEWS ITEMS AND ANNOUNCEMENTS ..... 496 ABSTRACTS OF CONTRIBUTED PAPERS .................•... 472, 481, 500 ERRATA . • . 589 INDEX TO ADVERTISERS . 608 MEETINGS Calendar of Meetings NOn:: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the c;Noticei) was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned.
  • Beurling-Type Density Criteria for System Identification

    Beurling-Type Density Criteria for System Identification

    1 Beurling-Type Density Criteria for System Identification Verner Vlaˇci´c∗, C´eline Aubel†, and Helmut B¨olcskei∗ ∗ETH Zurich, Switzerland †Swiss National Bank, Zurich, Switzerland Email: ∗[email protected], †[email protected], ∗[email protected] Abstract This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delay-Doppler shifts without a lattice (or other “geometry- discretizing”) constraint on the support set. Concretely, we show that a class of such LTV systems is identifiable whenever the upper uniform Beurling density of the delay-Doppler support sets, measured “uniformly over the class”, is strictly less than 1/2. The proof of this result reveals an interesting relation between LTV system identification and interpolation in the Bargmann-Fock space. Moreover, we show that this density condition is also necessary for classes of systems invariant under time- frequency shifts and closed under a natural topology on the support sets. We furthermore show that identifiability guarantees robust recovery of the delay-Doppler support set, as well as the weights of the individual delay-Doppler shifts, both in the sense of asymptotically vanishing reconstruction error for vanishing measurement error. I. INTRODUCTION Identification of deterministic linear time-varying (LTV) systems has been a topic of long-standing interest, dating back to the seminal work by Kailath [1] and Bello [2], and has seen significant renewed interest during the past decade [3]–[6]. This general problem occurs in many fields of engineering and science. Concrete examples include system identification in control theory and practice, the measurement of dispersive communication channels, and radar imaging.
  • Filters in C*-Algebras

    Filters in C*-Algebras

    Filters in C∗-Algebras Tristan Bice August 1, 2018 Abstract In this paper we analyze states on C∗-algebras and their relationship to filter-like structures of projections and positive elements in the unit ball. After developing the basic theory we use this to investigate the Kadison-Singer conjecture, proving its equivalence to an apparently quite weak paving conjecture and the existence of unique maximal centred extensions of projec- tions coming from ultrafilters on ω. We then prove that Reid’s positive answer to this for q-points in fact also holds for rapid p-points, and that maximal centred filters are obtained in this case. We then show that consistently such maximal centred filters do not exist at all meaning that, for every pure state φ on the Calkin algebra, there exist projections p and q such that φ(p)=1= φ(q), even though φ(r), for projections r p, q, is bounded strictly below 1. Lastly we investigate towers, using cardinal invariant equalities≤ to construct towers on ω that do and do not remain towers when canonically embedded into the Calkin algebra. Finally we show that consistently all towers on ω remain towers under this embedding.1 1 Introduction States on C∗-algebras and their relation to other objects in C∗-algebras, like closed left ideals and closed hereditary cones, have been studied for quite some time. Despite this, some basic questions about states remain unresolved, like the long-standing Kadison-Singer conjecture. This paper aims to provide another, more order theoretic, perspective on states by investigating their relation to certain filter-like objects.
  • A Note on the Invertibility of the Gabor Frame Operator on Certain

    A Note on the Invertibility of the Gabor Frame Operator on Certain

    A NOTE ON THE INVERTIBILITY OF THE GABOR FRAME OPERATOR ON CERTAIN MODULATION SPACES DAE GWAN LEE, FRIEDRICH PHILIPP, AND FELIX VOIGTLAENDER Abstract. We consider Gabor frames generated by a general lattice and a window function 1 d that belongs to one of the following spaces: the Sobolev space V1 = H (R ), the weighted 2 2 Rd H1 Rd ∩ L -space V2 = L1+|x|( ), and the space V3 = ( ) = V1 V2 consisting of all functions with finite uncertainty product; all these spaces can be described as modulation spaces with respect to suitable weighted L2 spaces. In all cases, we prove that the space of Bessel vectors in Vj is mapped bijectively onto itself by the Gabor frame operator. As a consequence, if the window function belongs to one of the three spaces, then the canonical dual window also belongs to the same space. In fact, the result not only applies to frames, but also to frame sequences. 1. Introduction Analyzing the time-frequency localization of functions is an important topic in harmonic analysis. Quantitative results on this localization are usually formulated in terms of function spaces such as Sobolev spaces, modulation spaces, or Wiener amalgam spaces. An especially 1 important space is the Feichtinger algebra S0 = M [7, 14] which has numerous remark- able properties; see, e.g., [4, Section A.6] for a compact overview. Yet, in some cases it is preferable to work with more classical spaces like the Sobolev space H1(Rd) = W 1,2(Rd), 2 2 Rd Rd C 2 the weighted L -space L1+|x|( ) = {f : → : (1+ |x|)f(x) ∈ L }, or the space H1 Rd 1 Rd 2 Rd 2 Rd ( ) = H ( ) ∩ L1+|x|( ) which consists of all functions g ∈ L ( ) with finite uncer- tainty product |x|2 · |g(x)|2 dx |ω|2 · |g(ω)|2 dω < ∞.
  • Promoting OR

    Promoting OR

    Volume 9 | Number 3 | September 2015 | ISSN 2223-4373 International Federation of Operational Research Societies NEWS What’s Inside Editorial Promoting OR From the IFORS AC 1 Promoting OR Sue Merchant, IFORS VP at large From the Editor At EURO this summer I was struck by the enthusiasm, amongst 2 Of Contributions and Transitions developing country delegates in particular, for undertaking the type Regional Conferences of practical OR which makes a real difference in industry, commerce 2 EURO 2015: Scottish Kilts and and government. However the enthusiasts reported a problem Research Clans with Impact which many of us have faced over the years – how to get business 3 OR People Make EURO: Glasgow and government to recognise that OR makes a difference and hence Hosts 27th EURO Conference recruit OR people. Indeed John Ranyard and Robert Fildes’ recent 4 Environment Takes Center Stage international study, with responses from 28 countries, confirmed that the lack of client at APORS 2015 awareness and understanding was a continuing and widespread problem. They stress the OR for Development importance of practitioner communities and OR societies in helping to drive awareness of OR 5 ICORD 2015 in countries across the world. 6 A Perfect Setting for a Workshop on Uplifting Living Conditions 6 Mexico Sets Stage for ICORD 2016 Various methods have been tried over the years to demonstrate how powerful OR is: for example, Obituaries INFORMS’ major campaign ‘The Science of 7 Heiner Müller-Merbach Better’ was initiated a few years ago and the UK 8 John Forbes Nash Jr. also adopted this approach, producing masses 9 Philippe Van Asbroek of promotional material, a DVD of OR activity Conferences in successful companies (which is available 9 IFORS 2020 Hosting Bids Shortlisted from the UK ORS) and setting up websites 10 13th EUROPT: Auld Reekie Blows ‘Science of Better.co.uk’ and ‘LearnaboutOR.