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Linear Infinite Particle Operators
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Author :V. A. Malyshev Robert Adol_fovich Minlos Publisher :American Mathematical Soc. ISBN 13 :9780821897607 Total Pages :314 pages Book Rating :4.8/5 (976 download)
Book Synopsis Linear infinite-particle operators by : V. A. Malyshev Robert Adol_fovich Minlos
Download or read book Linear infinite-particle operators written by V. A. Malyshev Robert Adol_fovich Minlos and published by American Mathematical Soc.. This book was released on 1995-02-13 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this book can be viewed in various ways. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the viewpoint of probability theory, it is concerned with the analysis of singular Markov processes; and, from the vantage point of mathematical physics, it analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory. Malyshev and Minlos describe two new approaches to the subject which have not been previously treated in monograph form. They also present background material which makes the book accessible and useful to researchers and graduate students working in functional analysis, probability theory, and mathematical physics.
Book Synopsis Linear Infinite-particle Operators by : Vadim Aleksandrovich Malyshev
Download or read book Linear Infinite-particle Operators written by Vadim Aleksandrovich Malyshev and published by American Mathematical Soc.. This book was released on 1995 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this book can be viewed in various ways. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the viewpoint of probability theory, it is concerned with the analysis of singular Markov processes; and, from the vantage point of mathematical physics, it analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory. Malyshev and Minlos describe two new approaches to the subject which have not been previously treated in monograph form. They also present background material which makes the book accessible and useful to researchers and graduate students working in functional analysis, probability theory, and mathematical physics.
Book Synopsis Linear Infinite-particle Operators by : Vadim Aleksandrovich Malyshev
Download or read book Linear Infinite-particle Operators written by Vadim Aleksandrovich Malyshev and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this book can be viewed in various ways. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the viewpoint of probability theory, it is concerned with the analysis of singular Markov processes; and, from the vantage point of mathematical physics, it analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory. Malyshev and Minlos describe two new approaches to the subject which have not been previously treated in monograph form. They also present background material w.
Book Synopsis Infinite-Dimensional Lie Groups by : Hideki Omori
Download or read book Infinite-Dimensional Lie Groups written by Hideki Omori and published by American Mathematical Soc.. This book was released on 2017-11-07 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.
Book Synopsis C * -Algebras and Elliptic Operators in Differential Topology by : I_U_ri_ Petrovich Solov_v Evgeni_ Vadimovich Troit_s_ki_
Download or read book C * -Algebras and Elliptic Operators in Differential Topology written by I_U_ri_ Petrovich Solov_v Evgeni_ Vadimovich Troit_s_ki_ and published by American Mathematical Soc.. This book was released on 2000-10-03 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of manifolds. The main topological application discussed in the book concerns the problem of the description of homotopy-invariant rational Pontryagin numbers of non-simply connected manifolds and the Novikov conjecture of homotopy invariance of higher signatures. The definition of higher signatures and the formulation of the Novikov conjecture are given in Chapter 3. In this chapter, the authors also give an overview of different approaches to the proof of the Novikov conjecture. First, there is the Mishchenko symmetric signature and the generalized Hirzebruch formulae and the Mishchenko theorem of homotopy invariance of higher signatures for manifolds whose fundamental groups have a classifying space, being a complete Riemannian non-positive curvature manifold. Then the authors present Solovyov's proof of the Novikov conjecture for manifolds with fundamental group isomorphic to a discrete subgroup of a linear algebraic group over a local field, based on the notion of the Bruhat-Tits building. Finally, the authors discuss the approach due to Kasparov based on the operator $KK$-theory and another proof of the Mishchenko theorem. In Chapter 4, they outline the approach to the Novikov conjecture due to Connes and Moscovici involving cyclic homology. That allows one to prove the conjecture in the case when the fundamental group is a (Gromov) hyperbolic group. The text provides a concise exposition of some topics from functional analysis (for instance, $C^*$-Hilbert modules, $K$-theory or $C^*$-bundles, Hermitian $K$-theory, Fredholm representations, $KK$-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over $C^*$-algebras), and from differential topology (characteristic classes). The book explains basic ideas of the subject and can serve as a course text for an introduction to the study of original works and special monographs.
Book Synopsis Sign-based Methods in Linear Statistical Models by : M. V. Boldin
Download or read book Sign-based Methods in Linear Statistical Models written by M. V. Boldin and published by American Mathematical Soc.. This book was released on 1997-04-22 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: For nonparametric statistics, the last half of this century was the time when rank-based methods originated, were vigorously developed, reached maturity, and received wide recognition. The rank-based approach in statistics consists in ranking the observed values and using only the ranks rather than the original numerical data. In fitting relationships to observed data, the ranks of residuals from the fitted dependence are used. The signed-based approach is based on the assumption that random errors take positive or negative values with equal probabilities. Under this assumption, the sign procedures are distribution-free. These procedures are robust to violations of model assumptions, for instance, to even a considerable number of gross errors in observations. In addition, sign procedures have fairly high relative asymptotic efficiency, in spite of the obvious loss of information incurred by the use of signs instead of the corresponding numerical values. In this work, sign-based methods in the framework of linear models are developed. In the first part of the book, there are linear and factor models involving independent observations. In the second part, linear models of time series, primarily autoregressive models, are considered.
Book Synopsis The Asymptotic Distribution of Eigenvalues of Partial Differential Operators by : Yu Safarov
Download or read book The Asymptotic Distribution of Eigenvalues of Partial Differential Operators written by Yu Safarov and published by American Mathematical Soc.. This book was released on 1996 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the subject of extensive research over a century, spectral asymptotics for partial differential operators attracted the attention of many outstanding mathematicians and physicists. This book studies the eigenvalues of elliptic linear boundary value problems and has as its main content a collection of asymptotic formulas describing the distribution of eigenvalues with high sequential numbers. Asymptotic formulas are used to illustrate standards eigenvalue problems of mechanics and mathematical physics. The volumes provides a basic introduction to all the necessary mathematical concepts and tools, such as microlocal analysis, billiards, symplectic geometry and Tauberian theorems. It is self-contained and would be suitable as a graduate text.
Book Synopsis Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics by : Boldrighini, Carlo
Download or read book Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics written by Boldrighini, Carlo and published by Universitätsverlag Potsdam. This book was released on 2020 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
Book Synopsis Qualitative topics in integer linear programming by : Valery N. Shevchenko
Download or read book Qualitative topics in integer linear programming written by Valery N. Shevchenko and published by American Mathematical Soc.. This book was released on 1996-10-15 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integer solutions for systems of linear inequalities, equations, and congruences are considered along with the construction and theoretical analysis of integer programming algorithms. The complexity of algorithms is analyzed dependent upon two parameters: the dimension, and the maximal modulus of the coefficients describing the conditions of the problem. The analysis is based on a thorough treatment of the qualitative and quantitative aspects of integer programming, in particular on bounds obtained by the author for the number of extreme points. This permits progress in many cases in which the traditional approach--which regards complexity as a function only of the length of the input--leads to a negative result.
Book Synopsis Probability Theory by : Anatoli_ I_A_kovlevich Dorogovt_s_ev
Download or read book Probability Theory written by Anatoli_ I_A_kovlevich Dorogovt_s_ev and published by American Mathematical Soc.. This book was released on 2011-06-21 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book of problems is intended for students in pure and applied mathematics. There are problems in traditional areas of probability theory and problems in the theory of stochastic processes, which has wide applications in the theory of automatic control, queuing and reliability theories, and in many other modern science and engineering fields. Answers to most of the problems are given, and the book provides hints and solutions for more complicated problems.
Book Synopsis Ordinary Differential Equations with Constant Coefficient by : Serge_ Konstantinovich Godunov
Download or read book Ordinary Differential Equations with Constant Coefficient written by Serge_ Konstantinovich Godunov and published by American Mathematical Soc.. This book was released on 1997-08-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of ordinary differential equations with constant coefficients. The exposition is based on ideas developing the Gelfand-Shilov theorem on the polynomial representation of a matrix exponential. Boundary value problems for ordinary equations, Green matrices, Green functions, the Lopatinskii condition, and Lyapunov stability are considered. This volume can be used for practical study of ordinary differential equations using computers. In particular, algorithms and computational procedures, including the orthogonal sweep method, are described. The book also deals with stationary optimal control systems described by systems of ordinary differential equations with constant coefficients. The notions of controllability, observability, and stabilizability are analyzed, and some questions on the matrix Lure-Riccati equations are studied.
Download or read book Real Analysis written by Satoru Igari and published by American Mathematical Soc.. This book was released on 1998 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to real analysis is based on a series of lectures by the author at Tohoku University. The text covers real numbers, the notion of general topology, and a brief treatment of the Riemann integral, followed by chapters on the classical theory of the Lebesgue integral on Euclidean spaces; the differentiation theorem and functions of bounded variation; Lebesgue spaces; distribution theory; the classical theory of the Fourier transform and Fourier series; and wavelet theory.
Book Synopsis Mathematics of Information and Coding by : Te Sun Han
Download or read book Mathematics of Information and Coding written by Te Sun Han and published by American Mathematical Soc.. This book was released on 2002 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide engineering and/or statistics students, communications engineers, and mathematicians with the firm theoretic basis of source coding (or data compression) in information theory. Although information theory consists of two main areas, source coding and channel coding, the authors choose here to focus only on source coding. The reason is that, in a sense, it is more basic than channel coding, and also because of recent achievements in source coding and compression. An important feature of the book is that whenever possible, the authors describe universal coding methods, i.e., the methods that can be used without prior knowledge of the statistical properties of the data. The authors approach the subject of source coding from the very basics to the top frontiers in an intuitively transparent, but mathematically sound, manner. The book serves as a theoretical reference for communication professionals and statisticians specializing in information theory. It will also serve as an excellent introductory text for advanced-level and graduate students taking elementary or advanced courses in telecommunications, electrical engineering, statistics, mathematics, and computer science.
Author :IA. G. Berkovich E. M. Zhmud' Publisher :American Mathematical Soc. ISBN 13 :9780821897829 Total Pages :414 pages Book Rating :4.8/5 (978 download)
Book Synopsis Characters of Finite Groups. Part 1 by : IA. G. Berkovich E. M. Zhmud'
Download or read book Characters of Finite Groups. Part 1 written by IA. G. Berkovich E. M. Zhmud' and published by American Mathematical Soc.. This book was released on 1997-12-02 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses character theory and its applications to finite groups. The work places the subject within the reach of people with a relatively modest mathematical background. The necessary background exceeds the standard algebra course with respect only to finite groups. Starting with basic notions and theorems in character theory, the authors present a variety of results on the properties of complex-valued characters and applications to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations and applications of monomial groups. The presentation is detailed, and many proofs of known results are new. Most of the results in the book are presented in monograph form for the first time. Numerous exercises offer additional information on the topics and help readers to understand the main concepts and results.
Book Synopsis Local Fields and Their Extensions: Second Edition by : Ivan B. Fesenko
Download or read book Local Fields and Their Extensions: Second Edition written by Ivan B. Fesenko and published by American Mathematical Soc.. This book was released on 2002-07-17 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to Mathematical Reviews, 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor -groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's -class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor -groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas.
Book Synopsis Second Order Elliptic Equations and Elliptic Systems by : Ya-Zhe Chen
Download or read book Second Order Elliptic Equations and Elliptic Systems written by Ya-Zhe Chen and published by American Mathematical Soc.. This book was released on 1998 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.
Author :A. N. Andrianov V. G. Zhuravlev Publisher :American Mathematical Soc. ISBN 13 :9780821897621 Total Pages :350 pages Book Rating :4.8/5 (976 download)
Book Synopsis Modular forms and Hecke operators by : A. N. Andrianov V. G. Zhuravlev
Download or read book Modular forms and Hecke operators written by A. N. Andrianov V. G. Zhuravlev and published by American Mathematical Soc.. This book was released on 1995-08-28 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
