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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 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.
Book Synopsis Modular Forms and Hecke Operators by : A. N. Andrianov
Download or read book Modular Forms and Hecke Operators written by A. N. Andrianov and published by American Mathematical Soc.. This book was released on 2016-01-29 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: he 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.
Download or read book Number Theory 1 written by Kazuya Kato and published by American Mathematical Soc.. This book was released on 2000 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.
Book Synopsis Algebraic Geometry 1 by : Kenji Ueno
Download or read book Algebraic Geometry 1 written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 1999 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.
Book Synopsis Best Approximation by Linear Superpositions (approximate Nomography) by : S. I͡A. Khavinson
Download or read book Best Approximation by Linear Superpositions (approximate Nomography) written by S. I͡A. Khavinson and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions D considered as a sub-space of the space of continous functions C(X) on a compact space X. Such properties as density of D in C(X), its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.
Book Synopsis Elliptic Functions and Elliptic Integrals by : Viktor Vasil_evich Prasolov
Download or read book Elliptic Functions and Elliptic Integrals written by Viktor Vasil_evich Prasolov and published by American Mathematical Soc.. This book was released on 1997-09-16 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis.
Author :Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina Publisher :American Mathematical Soc. ISBN 13 :9780821897836 Total Pages :208 pages Book Rating :4.8/5 (978 download)
Book Synopsis Local Properties of Distributions of Stochastic Functionals by : Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina
Download or read book Local Properties of Distributions of Stochastic Functionals written by Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina and published by American Mathematical Soc.. This book was released on 1998-02-10 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the distributions of functionals defined on the sample paths of stochastic processes. It contains systematic exposition and applications of three general research methods developed by the authors. (i) The method of stratifications is used to study the problem of absolute continuity of distribution for different classes of functionals under very mild smoothness assumptions. It can be used also for evaluation of the distribution density of the functional. (ii) The method of differential operators is based on the abstract formalism of differential calculus and proves to be a powerful tool for the investigation of the smoothness properties of the distributions. (iii) The superstructure method, which is a later modification of the method of stratifications, is used to derive strong limit theorems (in the variation metric) for the distributions of stochastic functionals under weak convergence of the processes. Various application examples concern the functionals of Gaussian, Poisson and diffusion processes as well as partial sum processes from the Donsker-Prokhorov scheme. The research methods and basic results in this book are presented here in monograph form for the first time. The text would be suitable for a graduate course in the theory of stochastic processes and related topics.
Book Synopsis Discreteness and Continuity in Problems of Chaotic Dynamics by : Michael L. Blank
Download or read book Discreteness and Continuity in Problems of Chaotic Dynamics written by Michael L. Blank and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the study of ergodic properties of so-called chaotic dynamical systems. One of the central topics is the interplay between deterministic and quasi-stochastic behaviour in chaotic dynamics and between properties of continuous dynamical systems and those of their discrete approximations. Using simple examples, the author describes the main phenomena known in chaotic dynamical systems, studying topics such as the operator approach in chaotic dynamics, stochastic stability, and the so-called coupled systems. The last two chapters are devoted to problems of numerical modeling of chaotic dynamics.
Book Synopsis Second Order Equations of Elliptic and Parabolic Type by : E. M. Landis
Download or read book Second Order Equations of Elliptic and Parabolic Type written by E. M. Landis and published by American Mathematical Soc.. This book was released on 1997-12-02 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity. The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.
Book Synopsis Problems and Theorems in Linear Algebra by : Viktor Vasil_evich Prasolov
Download or read book Problems and Theorems in Linear Algebra written by Viktor Vasil_evich Prasolov and published by American Mathematical Soc.. This book was released on 1994-06-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.
Book Synopsis Linear and Quasi-linear Equations of Parabolic Type by : Olʹga A. Ladyženskaja
Download or read book Linear and Quasi-linear Equations of Parabolic Type written by Olʹga A. Ladyženskaja and published by American Mathematical Soc.. This book was released on 1988 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Book Synopsis Control of Systems with Aftereffect by : Vladimir Borisovich Kolmanovskiĭ
Download or read book Control of Systems with Aftereffect written by Vladimir Borisovich Kolmanovskiĭ and published by American Mathematical Soc.. This book was released on 1996-01-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deterministic and stochastic control systems with aftereffect are considered. Necessary and sufficient conditions for the optimality of such systems are obtained. Various methods for the construction of exact and approximate solutions of optimal control problems are suggested. Problems of adaptive control for systems with aftereffect are analyzed. Numerous applications are described. The book can be used by researchers, engineers, and graduate students working in optimal control theory and various applications.
Book Synopsis Algebraic Topology: An Intuitive Approach by : Hajime Satō
Download or read book Algebraic Topology: An Intuitive Approach written by Hajime Satō and published by American Mathematical Soc.. This book was released on 1999 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.
Book Synopsis Linear Operators for Quantum Mechanics by : Thomas F. Jordan
Download or read book Linear Operators for Quantum Mechanics written by Thomas F. Jordan and published by Courier Corporation. This book was released on 2012-09-20 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.
Book Synopsis Semigroups of Linear Operators and Applications by : Jerome A. Goldstein
Download or read book Semigroups of Linear Operators and Applications written by Jerome A. Goldstein and published by Courier Dover Publications. This book was released on 2017-05-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.
