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Harmonic Analysis and Hypergroups
An underlying theme in this text is the notion of hypergroups, the theory of which has been developed and used in fields as diverse as special functions, differential equations, probability theory, representation theory, measure theory, Hopf algebras, and quantum groups. Other topics include the harmonic analysis of analytic functions, ergodic theory and wavelets.
Functional Analysis
In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces. While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis. It begins with the Gelfand theory of commutative Banach algebras, and proceeds to the Gelfand-Naimark theorem on commutat...
An Invitation to von Neumann Algebras
Why This Book: The theory of von Neumann algebras has been growing in leaps and bounds in the last 20 years. It has always had strong connections with ergodic theory and mathematical physics. It is now beginning to make contact with other areas such as differential geometry and K-Theory. There seems to be a strong case for putting together a book which (a) introduces a reader to some of the basic theory needed to appreciate the recent advances, without getting bogged down by too much technical detail; (b) makes minimal assumptions on the reader's background; and (c) is small enough in size to not test the stamina and patience of the reader. This book tries to meet these requirements. In any ...
Operator Algebras and Their Applications
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable C*-algebras, the Baum-Connes conjecture, E[subscript 0] semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Linear Algebra with Applications
Contributed articles.
Algebraic Methods in Operator Theory
The theory of operators stands at the intersection of the frontiers of modern analysis and its classical counterparts; of algebra and quantum mechanics; of spectral theory and partial differential equations; of the modern global approach to topology and geometry; of representation theory and harmonic analysis; and of dynamical systems and mathematical physics. The present collection of papers represents contributions to a conference, and they have been carefully selected with a view to bridging different but related areas of mathematics which have only recently displayed an unexpected network of interconnections, as well as new and exciting cross-fertilizations. Our unify ing theme is the al...
Applications of Hypergroups and Related Measure Algebras
`The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.
Nonnegative Matrices and Applications
This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications
Articles in this volume are based on talks given at the International Conference on Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications. The conference provided researchers in mathematics with the opportunity to discuss new developments in these rapidly growing fields. This book contains several excellent articles, both expository and original, with new and significant results. It is suitable for graduate students and researchers interested in Ring Theory,Diagram Algebras and related topics.
Azepines, Volume 43, Part 2
The Chemistry of Heterocyclic Compounds, since its inception, has been recognized as a cornerstone of heterocyclic chemistry. Each volume attempts to discuss all aspects – properties, synthesis, reactions, physiological and industrial significance – of a specific ring system. To keep the series up-to-date, supplementary volumes covering the recent literature on each individual ring system have been published. Many ring systems (such as pyridines and oxazoles) are treated in distinct books, each consisting of separate volumes or parts dealing with different individual topics. With all authors are recognized authorities, the Chemistry of Heterocyclic Chemistry is considered worldwide as the indispensable resource for organic, bioorganic, and medicinal chemists.
