Eigenfunction Expansions Operator Algebras And Riemannian Symmetric Spaces
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Eigenfunction Expansions Operator Algebras And Riemannian Symmetric Spaces
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Author : Robert M Kauffman
language : en
Publisher: CRC Press
Release Date : 1996-09-25
Eigenfunction Expansions Operator Algebras And Riemannian Symmetric Spaces written by Robert M Kauffman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-25 with Mathematics categories.
This Research Note pays particular attention to studying the convergence of the expansion and to the case where D is a family of partial differential operators. All operators in the natural von Neumann algebraassociated with D, and also unbounded operators affiliated with this algebra, are expanded simultaneously in terms of generalized eigenprojections. These are operators which carry a natural space associated with D into its dual. The elements of the range of these eigenprojections are the eigenfunctions, which solve the appropriate eigenvalue equations by duality. The spectral measure is abstractly defined, but its absolute continuity with respect to Hausdorf measure on the joint spectrum is shown to occur when the eigenfunctions are very well-behaved. Uniqueness results are given showing that any two expansions arise from each other by a simple change of variable. A considerable effort has been made to keep the book self-contained for readers with a background in functional analysis including a basic understanding of the theory of von Neumann algebras. More advanced topics in functional analysis, andan introduction to differential geometry and differential operator theory, mostly without proofs, are given in an extensive section on background material.
Recent Developments In Evolution Equations
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Author : G F Roach
language : en
Publisher: CRC Press
Release Date : 1995-04-28
Recent Developments In Evolution Equations written by G F Roach and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-28 with Mathematics categories.
This book presents the majority of talks given at an International Converence held recently at the University of Strathclyde in Glasgow. The works presented focus on the analysis of mathematical models of systems evolving with time. The main topics are semigroups and related subjects connected with applications to partial differential equations of evolution type. Topics of particular interest include spectral and asymptotic properties of semigroups, B evolution scattering theory, and coagulation fragmentation phenomena.
Classical Hypergeometric Functions And Generalizations
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Author : Howard S. Cohl
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-23
Classical Hypergeometric Functions And Generalizations written by Howard S. Cohl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Mathematics categories.
This is the first volume of a two-volume collection of recent research results related to hypergeometric functions. The second volume (Contemporary Mathematics, Volume 819) is titled Applications and $q$-Extensions of Hypergeometric Functions. This volume contains the proceedings of a minisymposium and two AMS special sessions in three conferences: Minisymposium on All Things Hypergeometric, $q$-series and Generalizations at the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-16), June 13–17, 2022, Centre de Recherches Mathématiques, Montréal, Québec, Canada; AMS Special Session on Hypergeometric Functions and $q$-series at the 2022 AMS Fall Western Sectional Meeting, October 22–23, 2022, University of Utah, Salt Lake City, Utah; and the AMS Special Session on Hypergeometric Functions, $q$-series and Generalizations, at the 2023 AMS Spring Eastern Virtual Sectional Meeting, April 1–2, 2023. This book provides a sampling of current mathematical research related to the Gauss hypergeometric function, and as well, its immediate generalizations and extensions. This includes the generalized hypergeometric functions that originated with Kummer, as well as such classical special functions as Lamé and Heun functions. It also includes certain functions relevant to algebraic geometry, such as hypergeometric functions over finite fields. All research articles come with extensive bibliographies and can serve as entry points to the current literature.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2001
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Representation Theory Of Lie Groups And Lie Algebras Proceedings Of Fuji Kawaguchiko Conference
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Author : Takeshi Kawazoe
language : en
Publisher: World Scientific
Release Date : 1992-08-07
Representation Theory Of Lie Groups And Lie Algebras Proceedings Of Fuji Kawaguchiko Conference written by Takeshi Kawazoe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-07 with categories.
The proceedings in this volume covers recent developments of representation theory of real Lie groups, Lie algebras, harmonic analysis on homogeneous spaces, their applications and related topics.
Representation Theory And Noncommutative Harmonic Analysis Ii
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Author : A.A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Representation Theory And Noncommutative Harmonic Analysis Ii written by A.A. Kirillov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the exponential function, the prob ability integral and so on. Elliptic integrals proved to be the most important. They are connected with rectification of arcs of certain curves. The remarkable idea of Abel to replace these integrals by the corresponding inverse functions led to the creation of the theory of elliptic functions. They are doubly periodic functions of a complex variable. This periodicity has led to consideration of the lattice of periods and to linear-fractional trans formations of the complex plane which leave this lattice invariant. The group of these transformations is isomorphic to the quotient group of the group 8L(2, Z) of unimodular matrices of the second order with integral elements with respect to its center. Investigation of properties of elliptic functions led to the study of automorphic functions and forms. This gave the first connec tion between the theory of groups and this important class of functions. The further development of the theory of automorphic functions was related to geometric concepts connected with the fact that the group of linear-fractional transformations with real elements can be realized as the group of motions of th the Lobachevskij plane. We also note that at the beginning of the 19 century Gauss used the group 8L(2, Z) in his papers on the theory of indeterminate quadratic forms.
Representation Theory And Automorphic Forms
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Author : T. N. Bailey
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Representation Theory And Automorphic Forms written by T. N. Bailey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR
Groups And Analysis
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Author : Katrin Tent
language : en
Publisher: Cambridge University Press
Release Date : 2008-10-16
Groups And Analysis written by Katrin Tent and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-16 with Mathematics categories.
Many areas of mathematics were deeply influenced or even founded by Hermann Weyl, including geometric foundations of manifolds and physics, topological groups, Lie groups and representation theory, harmonic analysis and analytic number theory as well as foundations of mathematics. In this volume, leading experts present his lasting influence on current mathematics, often connecting Weyl's theorems with cutting edge research in dynamical systems, invariant theory, and partial differential equations. In a broad and accessible presentation, survey chapters describe the historical development of each area alongside up-to-the-minute results, focussing on the mathematical roots evident within Weyl's work.
The British National Bibliography
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Author : Arthur James Wells
language : en
Publisher:
Release Date : 1996
The British National Bibliography written by Arthur James Wells and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Bibliography, National categories.
Symmetric Spaces And The Kashiwara Vergne Method
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Author : François Rouvière
language : en
Publisher: Springer
Release Date : 2014-10-14
Symmetric Spaces And The Kashiwara Vergne Method written by François Rouvière and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-14 with Mathematics categories.
Gathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject. Its goal is to: - motivate and explain the method for general Lie groups, reducing the proof of deep results in invariant analysis to the verification of two formal Lie bracket identities related to the Campbell-Hausdorff formula (the "Kashiwara-Vergne conjecture"); - give a detailed proof of the conjecture for quadratic and solvable Lie algebras, which is relatively elementary; - extend the method to symmetric spaces; here an obstruction appears, embodied in a single remarkable object called an "e-function"; - explain the role of this function in invariant analysis on symmetric spaces, its relation to invariant differential operators, mean value operators and spherical functions; - give an explicit e-function for rank one spaces (the hyperbolic spaces); - construct an e-function for general symmetric spaces, in the spirit of Kashiwara and Vergne's original work for Lie groups. The book includes a complete rewriting of several articles by the author, updated and improved following Alekseev, Meinrenken and Torossian's recent proofs of the conjecture. The chapters are largely independent of each other. Some open problems are suggested to encourage future research. It is aimed at graduate students and researchers with a basic knowledge of Lie theory.