Functional Analysis Book

Functional Analysis


  • Author : Peter D. Lax
  • Publisher : John Wiley & Sons
  • Release Date : 2014-08-28
  • Genre: Mathematics
  • Pages : 608
  • ISBN 10 : 9781118626740

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Functional Analysis Excerpt :

Includes sections on the spectral resolution and spectralrepresentation of self adjoint operators, invariant subspaces,strongly continuous one-parameter semigroups, the index ofoperators, the trace formula of Lidskii, the Fredholm determinant,and more. * Assumes prior knowledge of Naive set theory, linear algebra,point set topology, basic complex variable, and realvariables. * Includes an appendix on the Riesz representation theorem.

Functional Analysis Book

Functional Analysis


  • Author : R.E. Edwards
  • Publisher : Courier Corporation
  • Release Date : 2012-10-25
  • Genre: Mathematics
  • Pages : 800
  • ISBN 10 : 9780486145105

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Functional Analysis Excerpt :

Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.

Nonlinear Functional Analysis Book

Nonlinear Functional Analysis


  • Author : Klaus Deimling
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-11-11
  • Genre: Mathematics
  • Pages : 450
  • ISBN 10 : 9783662005477

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Nonlinear Functional Analysis Excerpt :

topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.

Functional Analysis Book

Functional Analysis


  • Author : Joseph Muscat
  • Publisher : Springer
  • Release Date : 2014-07-23
  • Genre: Mathematics
  • Pages : 420
  • ISBN 10 : 9783319067285

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Functional Analysis Excerpt :

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

Functional Analysis Book

Functional Analysis


  • Author : Theo Bühler
  • Publisher : American Mathematical Soc.
  • Release Date : 2018-08-08
  • Genre: Functional analysis
  • Pages : 466
  • ISBN 10 : 9781470441906

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Functional Analysis Excerpt :

It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and lin

Introductory Functional Analysis with Applications Book

Introductory Functional Analysis with Applications


  • Author : Erwin Kreyszig
  • Publisher : John Wiley & Sons
  • Release Date : 1991-01-16
  • Genre: Mathematics
  • Pages : 704
  • ISBN 10 : 9780471504597

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Introductory Functional Analysis with Applications Excerpt :

KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter HenriCi Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel TOPICS in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel TOPICS In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry

Functional Analysis Book

Functional Analysis


  • Author : Yuli Eidelman
  • Publisher : American Mathematical Soc.
  • Release Date : 2004
  • Genre: Mathematics
  • Pages : 322
  • ISBN 10 : 9780821836460

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Functional Analysis Excerpt :

The goal of this textbook is to provide an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively), and it is as self-contained as possible. The only prerequisites for the first part are minimal amounts of linear algebra and calculus. However, for the second course (Part II), it is useful to have some knowledge of topology and measure theory. Each chapter is followed by numerous exercises, whose solutions are given at the end of the book.

Functional Analysis Book

Functional Analysis


  • Author : George Bachman
  • Publisher : Courier Corporation
  • Release Date : 2012-09-26
  • Genre: Mathematics
  • Pages : 544
  • ISBN 10 : 9780486136554

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Functional Analysis Excerpt :

Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. 1966 edition.

Advanced Functional Analysis Book

Advanced Functional Analysis


  • Author : Eberhard Malkowsky
  • Publisher : CRC Press
  • Release Date : 2019-02-25
  • Genre: Mathematics
  • Pages : 446
  • ISBN 10 : 9780429809552

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Advanced Functional Analysis Excerpt :

Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research

Functional Analysis Book
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Functional Analysis


  • Author : P. K. Jain
  • Publisher : New Age International
  • Release Date : 1995
  • Genre: Functional analysis
  • Pages : 326
  • ISBN 10 : 812240801X

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Functional Analysis Excerpt :

The Book Is Intended To Serve As A Textbook For An Introductory Course In Functional Analysis For The Senior Undergraduate And Graduate Students. It Can Also Be Useful For The Senior Students Of Applied Mathematics, Statistics, Operations Research, Engineering And Theoretical Physics. The Text Starts With A Chapter On Preliminaries Discussing Basic Concepts And Results Which Would Be Taken For Granted Later In The Book. This Is Followed By Chapters On Normed And Banach Spaces, Bounded Linear Operators, Bounded Linear Functionals. The Concept And Specific Geometry Of Hilbert Spaces, Functionals And Operators On Hilbert Spaces And Introduction To Spectral Theory. An Appendix Has Been Given On Schauder Bases.The Salient Features Of The Book Are: * Presentation Of The Subject In A Natural Way * Description Of The Concepts With Justification * Clear And Precise Exposition Avoiding Pendantry * Various Examples And Counter Examples * Graded Problems Throughout Each ChapterNotes And Remarks Within The Text Enhances The Utility Of The Book For The Students.

Linear Functional Analysis Book

Linear Functional Analysis


  • Author : Bryan Rynne
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-14
  • Genre: Mathematics
  • Pages : 273
  • ISBN 10 : 9781447136552

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Linear Functional Analysis Excerpt :

This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.

Functional Analysis  Sobolev Spaces and Partial Differential Equations Book

Functional Analysis Sobolev Spaces and Partial Differential Equations


  • Author : Haim Brezis
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-11-02
  • Genre: Mathematics
  • Pages : 600
  • ISBN 10 : 9780387709147

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Functional Analysis Sobolev Spaces and Partial Differential Equations Excerpt :

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Functional Analysis Book

Functional Analysis


  • Author : Sergei Ovchinnikov
  • Publisher : Springer
  • Release Date : 2018-06-09
  • Genre: Mathematics
  • Pages : 205
  • ISBN 10 : 9783319915128

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Functional Analysis Excerpt :

This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Boundedness Theorem, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text. Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.

Functional Analysis for Probability and Stochastic Processes Book

Functional Analysis for Probability and Stochastic Processes


  • Author : Adam Bobrowski
  • Publisher : Cambridge University Press
  • Release Date : 2005-08-11
  • Genre: Mathematics
  • Pages : 393
  • ISBN 10 : 0521831660

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Functional Analysis for Probability and Stochastic Processes Excerpt :

This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.

Functional Analysis Book

Functional Analysis


  • Author : Kosaku Yosida
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-17
  • Genre: Mathematics
  • Pages : 468
  • ISBN 10 : 9783662117910

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Functional Analysis Excerpt :