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Author: Vladimir Semenovich Pugachev
Publisher: World Scientific
ISBN: 9789810237233
Category : Mathematics
Languages : en
Pages : 756
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Book Description
This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature. The material covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of applications of mathematics, as well as the simplicity of presentation, differentiates this book from others. About 300 examples and more than 500 problems are provided to help readers understand and master the theories presented. The list of references enables readers to explore those topics in which they are interested, and gather further information about applications used as examples in the book.Applications: Probability Theory and Statistics, Signal and Image Processing, Systems Analysis and Design.
Author: Vladimir Semenovich Pugachev
Publisher: World Scientific
ISBN: 9789810237233
Category : Mathematics
Languages : en
Pages : 756
Get Book Here
Book Description
This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature. The material covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of applications of mathematics, as well as the simplicity of presentation, differentiates this book from others. About 300 examples and more than 500 problems are provided to help readers understand and master the theories presented. The list of references enables readers to explore those topics in which they are interested, and gather further information about applications used as examples in the book.Applications: Probability Theory and Statistics, Signal and Image Processing, Systems Analysis and Design.
Author: Alberto Bressan
Publisher: American Mathematical Soc.
ISBN: 0821887718
Category : Mathematics
Languages : en
Pages : 265
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Book Description
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
Author: Vilmos Komornik
Publisher: Springer
ISBN: 1447168119
Category : Mathematics
Languages : en
Pages : 417
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Book Description
This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.
Author: J. Aczel
Publisher: Courier Corporation
ISBN: 0486445232
Category : Mathematics
Languages : en
Pages : 548
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Book Description
Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.
Author: Leonid P. Lebedev
Publisher: Springer Science & Business Media
ISBN: 0306483971
Category : Mathematics
Languages : en
Pages : 259
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Book Description
This book started its life as a series of lectures given by the second author from the 1970’s onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that state the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them. The requirements of lecture notes and books are vastly different. A book has to be complete (in some sense), self contained, and able to be read without the help of an instructor.
Author: Robert J. Zimmer
Publisher: University of Chicago Press
ISBN: 0226983382
Category : Mathematics
Languages : en
Pages : 169
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Book Description
Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.
Author: Manfred Einsiedler
Publisher: Springer
ISBN: 3319585401
Category : Mathematics
Languages : en
Pages : 626
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Book Description
This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.
Author: Александр Яковлевич Хелемский
Publisher: American Mathematical Soc.
ISBN: 9780821889695
Category : Mathematics
Languages : en
Pages : 496
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Book Description
The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
Author: V S Pugachev
Publisher: World Scientific Publishing Company
ISBN: 9813102926
Category : Mathematics
Languages : en
Pages : 752
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Book Description
This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature. The material covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of applications of mathematics, as well as the simplicity of presentation, differentiates this book from others. About 300 examples and more than 500 problems are provided to help readers understand and master the theories presented. The list of references enables readers to explore those topics in which they are interested, and gather further information about applications used as examples in the book. Applications: Probability Theory and Statistics, Signal and Image Processing, Systems Analysis and Design.
Author: Vladimir I. Bogachev
Publisher: Springer Nature
ISBN: 3030382192
Category : Mathematics
Languages : en
Pages : 602
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Book Description
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
