DOCSLIB.ORG

On the Verification of Linear Equations and the Identification of The

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Verification of Linear Equations and the Identification of The Operator Theory: Advances and Applications Vol. 170 Editor: I. Gohberg Editorial Office: S. T. Kuroda (Tokyo) School of Mathematical P. Lancaster (Calgary) Sciences L. E. Lerer (Haifa) Tel Aviv University B. Mityagin (Columbus) Ramat Aviv, Israel V. Olshevsky (Storrs) M. Putinar (Santa Barbara) Editorial Board: L. Rodman (Williamsburg) D. Alpay (Beer-Sheva) J. Rovnyak (Charlottesville) J. Arazy (Haifa) D. E. Sarason (Berkeley) A. Atzmon (Tel Aviv) I. M. Spitkovsky (Williamsburg) J. A. Ball (Blacksburg) S. Treil (Providence) A. Ben-Artzi (Tel Aviv) H. Upmeier (Marburg) H. Bercovici (Bloomington) S. M. Verduyn Lunel (Leiden) A. Böttcher (Chemnitz) D. Voiculescu (Berkeley) K. Clancey (Athens, USA) D. Xia (Nashville) L. A. Coburn (Buffalo) D. Yafaev (Rennes) R. E. Curto (Iowa City) K. R. Davidson (Waterloo, Ontario) Honorary and Advisory R. G. Douglas (College Station) Editorial Board: A. Dijksma (Groningen) C. Foias (Bloomington) H. Dym (Rehovot) P. R. Halmos (Santa Clara) P. A. Fuhrmann (Beer Sheva) T. Kailath (Stanford) B. Gramsch (Mainz) H. Langer (Vienna) J. A. Helton (La Jolla) P. D. Lax (New York) M. A. Kaashoek (Amsterdam) M. S. Livsic (Beer Sheva) H. G. Kaper (Argonne) H. Widom (Santa Cruz) Subseries: Advances in Michael Demuth Partial Differential Equations Technische Universität Clausthal Subseries editors: Germany Bert-Wolfgang Schulze Jerome A. Goldstein Universität Potsdam The University of Memphis, TN Germany USA Sergio Albeverio Nobuyuki Tose Universität Bonn Keio University, Yokohama Germany Japan Modern Operator Theory and Applications The Igor Borisovich Simonenko Anniversary Volume Ya. M. Erusalimsky I. Gohberg S. M. Grudsky V. Rabinovich N. Vasilevski Editors Birkhäuser Verlag Basel . Boston . Berlin Editors: Yakob M. Erusalimsky Vladimir Rabinovich Mechanical-Mathematics Department Instituto Politecnico Nacional Rostov State University ESIME Zacatenco Avenida IPN Zorge Str. 5 Mexico, D. F. 07738 Rostov-on-Don 344104 Mexico Russia e-mail: [email protected] e-mail: [email protected] Israel Gohberg Sergei M. Grudsky School of Mathematical Sciences Nikolai Vasilevski Raymond and Beverly Sackler Departamento de Matemáticas CINVESTAV Faculty of Exact Sciences Apartado Postal 14-740 Tel Aviv University 07000 Mexico, D.F. Ramat Aviv 69978 Mexico Israel e-mail: [email protected] e-mail: [email protected] [email protected] 0DWKHPDWLFV6XEMHFW&ODVVL¿FDWLRQ 45E, 45P05, 47G, 47L Library of Congress Control Number: 2006937466 Bibliographic information published by Die Deutsche Bibliothek 'LH'HXWVFKH%LEOLRWKHNOLVWVWKLVSXEOLFDWLRQLQWKH'HXWVFKH1DWLRQDOELEOLRJUD¿HGHWDLOHG bibliographic data is available in the Internet at <http://dnb.ddb.de>. ISBN 3-7643-7574-4 978-3-7643-7736-67574-4 Birkhäuser BirkhäuserVerlag, Basel –Verlag, Boston –Basel Berlin – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the PDWHULDOLVFRQFHUQHGVSHFL¿FDOO\WKHULJKWVRIWUDQVODWLRQUHSULQWLQJUHXVHRI LOOXVWUDWLRQVUHFLWDWLRQEURDGFDVWLQJUHSURGXFWLRQRQPLFUR¿OPVRULQRWKHUZD\VDQG storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2007 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF f Cover design: Heinz Hiltbrunner, Basel Printed in Germany ISBN-10: 3-7643-7736-4 e-ISBN-10: 3-7643-7737-2 ISBN-13: 978-3-7643-7736-6 e-ISBN-13: 978-3-7643-7737-3 9 8 7 6 5 4 3 2 1 www.birkhauser.ch Contents Portrait of Igor Borisovich Simonenko .................................... vii Introduction Ja.M. Jerusalimsky LifeandWorkofIgorBorisovichSimonenko ......................... 1 V.S. Pilidi OperatorsofLocalTypeandSingularIntegralOperators ............ 2 V.B. Levenshtam, S.M. Zenkovskaya An Averaging Method and its Application toHydrodynamicsProblems ......................................... 5 ListofPh.D.,whosesupervisorwasI.B.Simonenko ....................... 12 List of Ph.D., whose co-supervisor was I.B. Simonenko . 13 ListofD.Sc.,whoseadvisorwasI.B.Simonenko .......................... 13 PrincipalPublicationsofI.B.Simonenko .................................. 13 Contributions A.B. Antonevich Coefficients Averaging for Functional Operators GeneratedbyIrrationalRotation .................................... 27 A. B¨ottcher and D. Wenzel On the Verification of Linear Equations and the Identification oftheToeplitz-plus-HankelStructure ................................ 43 L.P. Castro, R. Duduchava and F.-O. Speck Asymmetric Factorizations of Matrix Functions on the Real Line . 53 R.G. Douglas and C. Foias On the Structure of the Square of a C0(1)Operator .................. 75 I. Feldman, N. Krupnik and A. Markus On the Connection Between the Indices of a Block Operator Matrix andofitsDeterminant............................................... 85 vi Contents I. Gohberg, M.A. Kaashoek and L. Lerer Quasi-commutativity of Entire Matrix Functions and theContinuousAnalogueoftheResultant ........................... 101 S.M. Grudsky Double Barrier Options Under L´evyProcesses ....................... 107 Yu.I. Karlovich A Local-trajectory Method and Isomorphism Theorems for Nonlocal C∗-algebras ............................................ 137 V. Kokilashvili, V. Paatashvili and S. Samko Boundedness in Lebesgue Spaces with Variable Exponent of theCauchySingularOperatoronCarlesonCurves ................... 167 V.B. Levenshtam On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces . 187 V.S. Rabinovich, S. Roch and B. Silbermann Finite Sections of Band-dominated Operators with AlmostPeriodicCoefficients ......................................... 205 N. Vasilevski On the Toeplitz Operators with Piecewise Continuous Symbols ontheBergmanSpace .............................................. 229 H. Widom Asymptoticsofa ClassofOperatorDeterminants .................... 249 Igor Borisovich Simonenko Operator Theory: Advances and Applications, Vol. 170, 1–26 c 2006 Birkh¨auser Verlag Basel/Switzerland Introduction Ja.M. Jerusalimsky Life and Work of Igor Borisovich Simonenko In August of 2005, the eminent Russian mathematician Dr. Igor Borisovich Simo- nenko celebrated his 70th Birthday. Igor Borisovich was born in Kiev (Ukraine, former USSR), where he spent his childhood. Along with the majority of his contemporaries, he experienced all the difficulties of wartime, evacuation and occupation, together with his mother in the steppes of Salsk. In 1943, upon returning to Lugansk with his mother, he began school, entering the third grade. In 1947 he left the primary school and entered a machine-building technical school. Having graduated from school in 1953, Igor first worked in a factory and then began to study at the Physics and Mathematics Department of the Rostov State University. The greatest influence on the young mathematician I.B. Simonenko was ren- dered by his teacher and supervisor, the brilliant scientist Fyodor Dmitrievich Gakhov, who managed to create three scientific schools: in Kazan, Rostov-on-Don and Minsk. In Igor Borisovich’s student years, the Physics and Mathematics Department of Rostov State University was on the rise. This had much to do with the pres- ence of the talented young experts in mechanics, the Moscow State University graduates I.I. Vorovich, N.N. Moiseev and L.A. Tolokonnikov (later academicians of the Russian Academy of Science) and the arrival at RSU in 1953 of professor F.D. Gakhov from Kazan. An active influence on the scientific life of the department was rendered by the scientific seminar “Boundary value problems” (headed by F.D. Gakhov) and the seminar “Theory of nonlinear operators” (headed by I.I. Vorovich and M.G. Khaplanov). The latter seminar became the source of ideas and methods in functional analysis and the starting point of a wide range of application of these methods by the Rostov mathematicians. In his 1961 Ph.D. thesis “Treaties in the theory of singular integral operators” I.B. Simonenko followed the classical methods of the school of his teacher. After defending this thesis, I.B. worked for several years at the RSU computer center. During this period, the results on the problems of electrostatics were obtained 2 Introduction (jointly with V.P. Zakharyuta and V.I. Yudovich), including a calculation of the capacity of condensers of complex form and dielectric materials with complex structure. In 1967, at the age of 32, six years after he defended his Ph.D. thesis, I.B. Si- monenko defended his thesis for a degree of Doctor of Science. In this thesis, entitled “Operators of local type and some other problems of the theory of linear operators,” he sharply turned towards the wide usage of the general methods of functional analysis. In 1971 professor I.B. Simonenko became the head of the Nu- merical Mathematics Chair. The following year this chair was split into two; I.B. became the head of one of them, the Chair of Algebra and Discrete Mathematics. The Chair of Algebra and Discrete Mathematics can be rightfully called the Chair of I.B. Simonenko. Here he worked together with his colleagues, students, and the students of his students. Here he fully developed his teaching talent. He lectured on “Algebra and geometry,” “Mathematical logic,” “Discrete mathemat- ics,” and “Mathematical analysis”. The scientific seminar of the Chair of Algebra and Discrete Mathematics is widely known both in Russia and abroad. Besides I.B. and his students, such well-known mathematicians as S.G. Mikhlin,
Load more

Recommended publications
  • Bart, Hempfling, Kaashoek. (Eds.) Israel Gohberg and Friends.. on The
    Israel Gohberg and Friends On the Occasion of his 80th Birthday Harm Bart Thomas Hempfling Marinus A. Kaashoek Editors Birkhäuser Basel · Boston · Berlin Editors: Harm Bart Marinus A. Kaashoek Econometrisch Instituut Department of Mathematics, FEW Erasmus Universiteit Rotterdam Vrije Universiteit Postbus 1738 De Boelelaan 1081A 3000 DR Rotterdam 1081 HV Amsterdam The Netherlands The Netherlands e-mail: [email protected] e-mail: [email protected] Thomas Hempfling Editorial Department Mathematics Birkhäuser Publishing Ltd. P.O. Box 133 4010 Basel Switzerland e-mail: thomas.hempfl[email protected] Library of Congress Control Number: 2008927170 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. ISBN 978-3-7643-8733-4 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8733-4 e-ISBN 978-3-7643-8734-1 9 8 7 6 5 4 3 2 1 www.birkhauser.ch Contents Preface.......................................................................ix CongratulationsfromthePublisher...........................................xii PartI.MathematicalandPhilosophical-MathematicalTales...................1 I.
    [Show full text]
  • Reproducing Kernel Krein Spaces of Analytic Functions and Inverse Scattering
    Chapman University Chapman University Digital Commons Mathematics, Physics, and Computer Science Science and Technology Faculty Articles and Faculty Articles and Research Research 10-1985 Reproducing Kernel Krein Spaces of Analytic Functions and Inverse Scattering Daniel Alpay Follow this and additional works at: https://digitalcommons.chapman.edu/scs_articles Part of the Algebra Commons, Analysis Commons, and the Other Mathematics Commons Reproducing Kernel Krein Spaces of Analytic Functions and Inverse Scattering Comments This is Dr. Daniel Alpay's thesis for the Doctor of Philosophy from the Weizmann Institute of Science in Rehovot, Israel, in October 1985. Copyright The author REPRODUCING KERNEL KREIN SPACES OF ANALYTIC FUNCTIONS AND INVERSE SCATTERING THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY by DANIEL ALPAY Submitted to the Scientific Council of the Weizmann Institute of Science, Rehovot, Israel. October 1985. ABSTRACT The purpose of this thesis is to study certain reproducing kernel Krein spaces of analytic functions, the relationships between these spaces and an inverse scattering problem associated with matrix valued functions of bounded type, and an operator model. Roughly speaking, these results correspond to a generalization of earlier investigations on the applications of de Branges' theory of reproducing kernel Hilbert spaces of analytic functions to the inverse scattering problem for a matrix valued function of the Schur class. The present work considers first a generalization of a portion of de Branges' theory to Krein spaces. We then formulate a general inverse scattering problem which includes as a special case the more classical inverse scattering problem of finding linear fractional representations of a given matrix valued function of the Schur class and use the theory alluded to above to obtain solutions to this problem.
    [Show full text]
  • Final Program Mathematical Theory of Networks and Systems
    MTNS { 2002 1 Final Program Fifteenth International Symposium on Mathematical Theory of Networks and Systems University of Notre Dame, South Bend, Indiana, USA August 12-16, 2002. www.nd.edu/~mtns/ MTNS { 2002 2 Organizing Committee of MTNS 2002 SYMPOSIUM CHAIR Victor Vinnikov (Israel) Joachim Rosenthal (USA) Xiaochang Wang (USA) Shigeru Yamamoto (Japan) PUBLICATION CHAIR Sandro Zampieri (Italy) David S. Gilliam (USA) STEERING COMMITTEE PROGRAM COMMITTEE V. Blondel (Belgium) Mark Alber (USA) C.I. Byrnes (USA) Joe Ball (USA) R. Curtain (The Netherlands) Vincent Blondel (Belgium) B.N. Datta (USA) Tyrone Duncan (USA) P. Dewilde (The Netherlands) Avraham Feintuch (Israel) P. Van Dooren (Belgium) David Forney (USA) H. Dym (Israel) Krzysztof Galkowski (Poland) A. El Jay (France) Tryphon Georgiou (USA) M. Fliess (France) Heide Gluesing-Luerssen (Germany) P. Fuhrmann (Israel) Koichi Hashimoto (Japan) I. Gohberg (Israel) Bernard Hanzon (The Netherlands) U. Helmke (Germany) Diederich Hinrichsen (Germany) J.W. Helton (USA) Aleksandar Kavcic (USA) A. Isidori (Italy) Matthias Kawski (USA) M.A. Kaashoek (The Netherlands) Belinda King (USA) H. Kimura (Japan) Wolfgang Kliemann (USA) A.J. Krener (USA) Margreet Kuijper (Australia) A.B. Kurzhansky (Russia) Naomi Leonard (USA) A. Lindquist (Sweden) Daniel Liberzon (USA) C.F. Martin (USA) Wei Lin (USA) G. Picci (Italy) Brian Marcus (USA) A.C.M. Ran (The Netherlands) Volker Mehrmann (Germany) A. Rantzer (Sweden) Raimund Ober (USA) J. Rosenthal (USA) Dieter Praetzel-Wolters (Germany) J.H. van Schuppen (The Netherlands) Eric Rogers (United Kingdom) Y. Yamamoto (Japan) Pierre Rouchon (France) Hans Schumacher (The Netherlands) HONORARY MEMBERS Mark Shayman (USA) C.A. Desoer (USA) Rodolphe Sepulchre (Belgium) R.W.
    [Show full text]
  • University of Groningen Heinz Langer and His Work Dijksma, Aad
    University of Groningen Heinz Langer and his Work Dijksma, Aad; Gohberg, Israel Published in: EPRINTS-BOOK-TITLE IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2008 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Dijksma, A., & Gohberg, I. (2008). Heinz Langer and his Work. In EPRINTS-BOOK-TITLE University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license. More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne- amendment. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 30-09-2021 Heinz Langer and his Work Aad Dijksma and Israel Gohberg 1.
    [Show full text]
  • Ball2018 Chapter Remembering Leiba
    VU Research Portal Remembering Leiba Rodman 1949–2015, at IWOTA 2015 Ball, J. A.; Kaashoek, M. A.; Ran, A. C.M.; Spitkovsky, I. M. published in Operator Theory in Different Settings and Related Applications 2018 DOI (link to publisher) 10.1007/978-3-319-62527-0_1 document version Publisher's PDF, also known as Version of record document license Article 25fa Dutch Copyright Act Link to publication in VU Research Portal citation for published version (APA) Ball, J. A., Kaashoek, M. A., Ran, A. C. M., & Spitkovsky, I. M. (2018). Remembering Leiba Rodman 1949–2015, at IWOTA 2015. In R. Duduchava, & M. A. Kaashoek (Eds.), Operator Theory in Different Settings and Related Applications: 26th IWOTA, Tbilisi, July 2015 (pp. 3-12). (Operator Theory: Advances and Applications; Vol. 262, No. 3-12). Springer International Publishing Switzerland. https://doi.org/10.1007/978-3-319-62527-0_1 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
    [Show full text]
  • Recollections of the MTNS
    mtnsStory.tex October 19, 2012 Recollections of the MTNS Whats Up? Margreta Kuijper suggested on the occasion of the 20th meeting of the MTNS we have some effort toward recovering the history of the organization (pardon the oxymoron). This occasion being the first effort along historical lines, appropriate now is gathering data, gathering stories, detecting some of the trends and then having a beer. Later someone can put a balance in these descriptions and distill accurate advice, so others can avoid our mistakes. Our story starts with Bill Helton's recollections of the liftoff of the MTNS from nothing to becoming one of the world's most prominent theoretical systems meeting. Slides from Bill's talk.1 Chris Byrnes' favorite maxim was \if your only tool is a hammer then every problem is a nail", from which it follows that operator theory will loom large in Bill's story and other important subjects will appear to be specs at the periphery. Joe Ball next recalls the Delft 1979 meeting and some of its antecedents. After that, Anders Lindquist tells the wild tale of Stockholm in 1985. Yutaka Yamamoto describes the history of MTNS in Japan which started in 1991. After that Joachim Rosenthal describes how coding theory flowed into the MTNS and the Notre Dame meeting in 2002. These notes were assembled by Bill Helton, so the gross distortions you see should be attributed to him. There is a slot in this .tex file for those with their own accounts, so all observers are encouraged to contribute. Please send your tall tales to Bill.
    [Show full text]
  • Otices of The
    OTICES OF THE AMERICAN MATHEMATICAL SOCIETY Rademacher on J( 1), Poincare Series of Nonpositive Weights and the Eichler Cohomology Marvin I. Knopp page 385 Columbus Meeting (August 8-11) page 447 First Announcem~t The National Science Foundation Budget Request for Fiscal 1991 page 394 Mathematics Outside of Mathematics Departments page 408 APRIL 1990, VOLUME 37, NUMBER 4 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting, insofar as is possible. and annual meetings are joint meetings of the Mathematical Associ­ Abstracts should be submitted on special forms which are available in ation of America and the American Mathematical Society. The meet­ many departments of mathematics and from the headquarters office ing dates which fall rather far in the future are subject to change; this of the Society. Abstracts of papers to be presented at the meeting is particularly true of meetings to which no numbers have been as­ must be received at the headquarters of the Society in Providence, signed. Programs of the meetings will appear in the issues indicated Rhode Island, on or before the deadline given below for the meet­ below. First and supplementary announcements of the meetings will ing. Note that the deadline for abstracts for consideration for pre­ have appeared in earlier issues. sentation at special sessions is usually three weeks earlier than that Abstracts of papers presented at a meeting of the Society are pub­ specified below.
    [Show full text]
  • In Memoriam Israel Gohberg August 23, 1928–October 12, 2009 ∗ Harm Bart A, , Harry Dym B, Rien Kaashoek C, Peter Lancaster D, Alexander Markus E, Leiba Rodman F
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Linear Algebra and its Applications 433 (2010) 877–892 Contents lists available at ScienceDirect Linear Algebra and its Applications journal homepage: www.elsevier.com/locate/laa In memoriam Israel Gohberg August 23, 1928–October 12, 2009 ∗ Harm Bart a, , Harry Dym b, Rien Kaashoek c, Peter Lancaster d, Alexander Markus e, Leiba Rodman f a Erasmus University Rotterdam, Rotterdam, The Netherlands b Weizmann Institute of Science, Rehovot 76100, Israel c VU University, Amsterdam, The Netherlands d University of Calgary, Calgary, Alberta, Canada e Ben-Gurion-University of the Negev, Beer Sheva, Israel f College of William and Mary, Williamsburg, VA 23187-8795, USA ARTICLE INFO ABSTRACT Article history: This obituary for Israel Gohberg consists of a general introduc- Received 28 October 2009 tion, separate contributions of the six authors, all of whom worked Accepted 3 March 2010 closely with him, and a final note. The material gives an impression Available online 2 April 2010 of the life of this great mathematician, of his monumental impact in Submitted by H. Schneider the areas he worked in, of how he cooperated with colleagues, and of his ability to stimulate people in their mathematical activities. AMS classification: 01A-65 01A-70 01A-74 15-03 45-03 46-03 47-03 65-03 93-03 Keywords: History of mathematics Matrix and operator polynomials Rational matrix functions State space method in analysis ∗ Corresponding author. E-mail addresses: [email protected] (H. Bart), [email protected] (H.
    [Show full text]
  • From Sommerfeld Problems to Operator Factorisation
    1 Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications Summer School at Isaac Newton Institute, Cambridge, 5-9 August 2019 Frank-Olme Speck T´ecnico,U Lisboa, Portugal From Sommerfeld problems to operator factorisation Contents First Last J I Back Close Full Screen 2 1 Introduction The original Sommerfeld diffraction problem has been solved by series expansion in 1896 NZS04*,Som96 and some 50 years later by the so-called Wiener-Hopf technique in the 1940s, see Jon64,Nob58,Wei69. Another 40 years later it has been proved to be well posed in the sense of Hadamard Had02 in certain Sobolev space settings MS89,S86 Moreover the resolvent operator has been identified as an explicit formula based upon operator factorisation in the sense of Shinbrot in the context of a wider class of problems DevShi69,Shi64,S85,S86. *[NZS04] R.J. Nagem, M. Zampolli, and G. Sandri, Mathematical Theory of Diffraction. Birkh¨auser,Boston 2004. In eight sections we shall address the following questions: Contents First Last J I Back Close Full Screen 3 Part I • How can we consider the classical Wiener-Hopf procedure as an operator factorisation (OF) and what is the profit of that interpretation? • What are the characteristics of Wiener-Hopf operators occurring in Sommerfeld half-plane problems and their features in terms of functional analysis? Part II • What are the most relevant methods of constructive matrix fac- torisation in Sommerfeld problems? • How does OF appear generally in linear boundary value and transmission
    [Show full text]
  • Death of a Schoolmaster
    NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY ERCOM Feature History Interview MPI-Leipzig Chaotic vibrations Edinburgh Math Soc Pierre Cartier p. 35 p. 19 p. 27 p. 31 December 2009 Issue 74 ISSN 1027-488X S E European M M Mathematical E S Society ems Dec_09.qxp 24/11/2009 08:39 Page 1 MaMathemathematicstics Book Bookss 1 FROMFROM OO XFXF ORDORD Introduction to Applied Algebraic Oxford University Press is pleased to announce that all Systems EMS members can benefit from a 20% discount on a large Norman R Reilly range of our Mathematics books. For more information This upper level undergraduate textbook please visit: www.oup.com/uk/sale/science/ems provides a modern view of algebra with an eye to new applications that have arisen in recent years. NEW ! 2009 | 524 pp | Hardback |978-0-19-536787-4| £50.00 The Oxford Handbook of Membrane Computing EMS member price: £40.00 Edited by Gheorghe Paun, Grzegorz Rozenberg and Arto Salomaa Thermoelasticity with Finite Wave Provides both a comprehensive survey Speeds of available knowledge and established Józef Ignaczak and Martin Ostoja Starzewski research topics, and a guide to recent Extensively covers the mathematics of developments in the field, covering the two leading theories of hyperbolic subject from theory to applications. thermoelasticity: the Lord Shulman Dec. 2009 | 696 pp | Hardback |978-0-19-955667-0 | £85.00 theory, and the Green Lindsay theory. EMS member price: £68.00 Oxford Mathematical Monographs NEW ! Oct. 2009 | 432 pp | Hardback |978-0-19-954164-5 | £70.00 Solitons, Instantons, and Twistors EMS member price: £56.00 Maciej Dunajski Provides a self contained and accessible introduction to elementary twistor Differential Equations with Linear theory; a technique for solving Algebra differential equations in applied Matthew R.
    [Show full text]