Edgment of the Services Rendered by the Following Persons Who Have Refereed Papers: R
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NOTES and REMARKS CHAPTER 1. the Material of Chapter 1 Is
NOTES AND REMARKS CHAPTER 1. The material of Chapter 1 is accessible in a number of sources. We refer the reader to various monographs and textbooks rather than to original sources. An early, but very readable, treatment is Schatten's monograph [154]. Chapter 9 in Diestel and Uhl [55] is also helpful. Among textbooks which treat the tensor product of linear topological spaces, are those of Treves [165], Day [41], Kothe [113], and Schaefer [153]. The article by Gilbert and Leih [61] contains a succinct account of tensor-product theory. The norms a p discussed in 1.43 to 1.46 were introduced independently by Saphar [152] and Chevet [36]. The paper of Saphar [151] contains a wealth of information about them. The proof of the triangle inequality in 1.46 is from [151]. The isomorphism theorem 1.52 was apparently obtained independently by Chevet [35] and Persson [140]. CHAPTER 2. The first half of Chapter 2 deals with the proximinality of G <2> Y in X 0 a Y, where X and Y are Banach spaces, G is a subspace of X, and a is a crossnorm. Results 2.1 to 2.3 and 2.5 to 2.7 are from Franchetti and Cheney [61]. The distance formula in C(S, Y) (2.4) was given, along with many other important results, by Buck [25]. The part of 2.4 which refers to £00 (S, Y) is from von Golitschek and Cheney [16]. The results 2.10 to 2.13, concerning proximinality in spaces LdS, Y), are contained implicitly or explicitly in Khalil [112]. -
THE SUMMER MEETING in CHICAGO the Forty-Seventh
THE SUMMER MEETING IN CHICAGO The forty-seventh Summer Meeting of the Society and the twenty- third Colloquium were held at the University of Chicago, Chicago, Illinois, Tuesday to Saturday, September 2-6, 1941. The Mathemati cal Association of America met on Monday morning and afternoon, and jointly with the Society on Wednesday afternoon. The Institute of Mathematical Statistics held sessions Tuesday morning and after noon and Wednesday afternoon. The Econometric Society met Tues day, Wednesday and Thursday mornings and Tuesday afternoon. The meeting was held in connection with the Fiftieth Anniversary Celebration of the University of Chicago, and on Tuesday morning Mr. Frederic Woodward, vice president emeritus of the University and director of the Celebration, gave a greeting and welcome to the mathematicians. As a part of the Fiftieth Anniversary Celebration, the University of Chicago collaborated with the Society in arranging a special program of lectures and conferences. The number of papers presented at this meeting is the largest in the history of the Society and the attendance the second largest. Six hundred thirty-five persons registered including the following four hundred twenty-four members of the Society: C. R. Adams, V. W. Adkisson, R. P. Agnew, A. A. Albert, G. E. Albert, C. B. Allendoerfer, Warren Ambrose, M. R. Anderson, T. W. Anderson, K. J. Arnold, Emil Artin, W. L. Ayres, H. M. Bacon, R. M. Ballard, J. D. Bankier, R. W. Barnard, I. A. Barnett, Walter Bartky, R. E. Basye, Harry Bateman, R. A. Beaumont, M. M. Beenken, A. A. Bennett, D. L. Bernstein, R. M. Besancon, E. -
Mathematical Genealogy of the University of Michigan-Dearborn
Joseph Johann von Littrow William Ernest Schmitendorf Tosio Kato Erhard Weigel Ancestors of UM-Dearborn Faculty Werner Güttinger Albert Turner Bharucha-Reid George Yuri Rainich Christian Otto Mohr Franz Josef Ritter von Gerstner Purdue University 1968 University of Tokyo 1951 Universität Leipzig 1650 in Mathematics and Statistics Mathematical Genealogy of the University of Michigan-Dearborn Kazan State University 1913 Department of Mathematics and Statistics Secondary The Mathematics Genealogy Project is a service of Advisor North Dakota State University and the American Mathematical Society. Nikolai Dmitrievich Brashman John Riordan, M.S. Bruce Scott Elenbogen Preben Kjeld Alsholm Frank Jones Massey Gottfried Wilhelm Leibniz http://www.genealogy.math.ndsu.nodak.edu/ Otto Mencke Dieter Armbruster Ranganatha Srinivasan Ruel Vance Churchill August Föppl Bernard(us) Placidus Johann Nepomuk Bolzano Moscow State University 1834 University of Michigan 1956 Northwestern University 1981 University of California, Berkeley 1972 University of California, Berkeley 1971 Universität Altdorf 1666 Universität Leipzig 1665, 1666 Universität Stuttgart 1985 Wayne State University 1965 University of Michigan 1929 Universität Stuttgart University of Prague 1805 Former UM-Dearborn Faculty in Mathematics and Statistics Primary Pafnuty Lvovich Chebyshev Jacob Bernoulli Johann Christoph Wichmannshausen Rama Chidambaram John Albert Gillespie Earl D. Rainville Ludwig Prandtl Franz Moth Józef Maximilian Petzval Advisor University of St. Petersburg 1849 Universität Basel 1684 Universität Leipzig 1685 Arizona State University 2003 Temple University 1982 University of Michigan 1939 Ludwig-Maximilians-Universität München 1899 University of Prague 1822 University of Pest 1832 Current UM-Dearborn Faculty in Mathematics and Statistics Andrei Andreyevich Markov Johann Bernoulli Christian August Hausen James Ward Brown H F. -
Distinguished Mathematical Research Award Recipients
Math Times Department of Mathematics Fall 2003 Distinguished Mathematical State Farm Foundation Research award recipients Professorship established Professors Derek Robinson and Zhong-Jin Ruan grant of $500,000 from the State Farm have been awarded 2003-2005 Distinguished A Companies Foundation has resulted in the Mathematical Research Awards. These awards, given by establishment of the State Farm Companies the department for the first time in Fall 2001, have a dual Professorship in Actuarial Science at the University purpose. The first purpose is to recognize senior members of Illinois. The grant is an endowment: the principal of the faculty for their outstanding achievements and to will remain intact, with income used to enhance the provide them more time to focus on their research salary and provide other benefits to a person named activities. The second purpose is to honor distinguished State Farm Scholar or State Farm Professor. Such department faculty members of the past for their endowed positions are among the best ways for a contributions to mathematics as a whole and to the university to attract and retain talented faculty, and Department of Mathematics at the University of Illinois honor both the recipient and the institution whose name in particular. Each year the awards are presented by the they carry. The State Farm Companies Foundation’s Executive Committee to at most two senior members of gift is a wonderful example of corporate citizenship, the department. and we at Illinois are deeply grateful for it. erek Robinson’s Distinguished Mathematical At a ceremony in the Illini Union on September D Research Award is given in memory of William W. -
Measures and Functions in Locally Convex Spaces
Measures and functions in locally convex spaces by Rudolf Gerrit Venter Submitted in partial fulfillment of the requirements for the degree Philosophiæ Doctor in the Department of Mathematics and Applied Mathematics in the Faculty of Natural and Agricultural Sciences University of Pretoria Pretoria July 21, 2010 Declaration I, the undersigned, hereby declare that the thesis submitted herewith for the degree Philosophiæ Doctor to the University of Pretoria contains my own, independent work and has not been submitted for any degree at any other university. Name: Rudolf Gerrit Venter Date: July 21, 2010 ii Dankbetuigings Ek is groot dank aan al my familie verskuldig: Ma, Marlien, Ouma en Tannie San, Tan- nie Loom en Oom Hennie, Oom Gerrit en Tannie Pat, Ralph, Charlotte, Jan-Andries en Ferdinand. Professor Johan Swart, dankie vir al jou advies, hulp en ondersteuning. Professor Joe Diestel, thank you for the Liapounoff-problem, your advice and valuable insight. Ek bedank al my voormalige kollegas in die Departement van Wiskunde en Toegepaste Wiskunde by die Noord-Wes Universiteit in Potchefstroom. Julle het 'n baie aangename werksatmosfeer geskep. Groot dank is verskuldig aan Professors Koos Grobler, Jan Fourie en Gilbert Groenewald. Dankie Anton, Jean, Hans-Werner, Wha-Suck, Gusti, Mienie en Charles Maepa vir julle ondersteuning. Die Here. iii Contents Introduction 1 1 Preliminaries 4 1.1 Locally Convex Spaces . 4 1.1.1 Quotient and Normed Spaces . 7 1.2 Vector Measures . 8 1.2.1 Spaces of Measures . 8 1.2.2 Stone Representation . 9 1.2.3 p-semivariation . 9 1.2.4 Bartle-Dunford-Schwartz-type Theorems . -
Global Automorphic Sobolev Theory and the Automorphic Heat Kernel
GLOBAL AUTOMORPHIC SOBOLEV THEORY AND THE AUTOMORPHIC HEAT KERNEL AMY T. DECELLES Abstract. Heat kernels arise in a variety of contexts including probability, geometry, and functional analysis; the automorphic heat kernel is particularly important in number theory and string theory. The typical construction of an automorphic heat kernel as a Poincar´eseries presents analytic difficulties, which can be dealt with in special cases (e.g. hyperbolic spaces) but are often sidestepped in higher rank by restricting to the compact quotient case. In this paper, we present a new approach, using global automorphic Sobolev the- ory, a robust framework for solving automorphic PDEs that does not require any simplifying assumptions about the rank of the symmetric space or the compactness of the arithmetic quotient. We construct an automorphic heat kernel via its automorphic spectral expansion in terms of cusp forms, Eisen- stein series, and residues of Eisenstein series. We then prove uniqueness of the automorphic heat kernel as an application of operator semigroup theory. Finally, we prove the smoothness of the automorphic heat kernel by proving that its automorphic spectral expansion converges in the C∞-topology. 1. Introduction Heat kernels arise in many contexts in mathematics and physics, so many that Jorgenson and Lang have called the heat kernel “ubiquitous” [23]. Automorphic heat kernels are important in physics and number theory: applications include multiloop amplitudes of certain bosonic strings [8], asymptotic formulas for spectra of arithmetic