# Search Results for "functional-analysis"

## Functional Analysis

**Author**: George Bachman,Lawrence Narici**Publisher:**Courier Corporation**ISBN:**0486136558**Category:**Mathematics**Page:**544**View:**3057

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.

## Functional Analysis

**Author**: Kösaku Yosida**Publisher:**Springer Science & Business Media**ISBN:**3642618596**Category:**Mathematics**Page:**504**View:**5300

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe maticians, both pure and applied. The reader may pass, e. g. , from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

## Functional Analysis

*Entering Hilbert Space*

**Author**: Vagn Lundsgaard Hansen**Publisher:**World Scientific**ISBN:**9812565639**Category:**Mathematics**Page:**136**View:**7581

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo? logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SoBOLEV and L. ScmVARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe? maticians, both pure and applied. The reader may pass e. g. from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integ-ration of the Equation of Evolution). Such materials as 'Weak Topologies and Duality in Locally Convex Spaces' and 'Nuclear Spaces' are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

## Functional Analysis

**Author**: Yurij M. Berezansky,Zinovij G. Sheftel,Georgij F. Us**Publisher:**Birkhäuser**ISBN:**3034891857**Category:**Mathematics**Page:**426**View:**2681

"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.

## Functional Analysis

**Author**: A. R. Vasishtha, J. N. Sharma**Publisher:**Krishna Prakashan Media**ISBN:**N.A**Category:****Page:**429**View:**7283

## Elementary Functional Analysis

**Author**: Barbara MacCluer**Publisher:**Springer Science & Business Media**ISBN:**0387855297**Category:**Mathematics**Page:**208**View:**3748

Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A.M. Vershik ([45], p. 438). This text evolved from the content of a one semester introductory course in fu- tional analysis that I have taught a number of times since 1996 at the University of Virginia. My students have included ?rst and second year graduate students prep- ing for thesis work in analysis, algebra, or topology, graduate students in various departments in the School of Engineering and Applied Science, and several und- graduate mathematics or physics majors. After a ?rst draft of the manuscript was completed, it was also used for an independent reading course for several und- graduates preparing for graduate school.

## Functional Analysis

**Author**: E. Suhubi**Publisher:**Springer Science & Business Media**ISBN:**9401701415**Category:**Mathematics**Page:**691**View:**1673

Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.

## Functional Analysis

*An Introduction*

**Author**: Yuli Eidelman,Vitali D. Milman,Antonis Tsolomitis**Publisher:**American Mathematical Soc.**ISBN:**0821836463**Category:**Mathematics**Page:**322**View:**996

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.

## I: Functional Analysis

**Author**: Michael Reed,Michael (Duke University Reed, North Carolina),REED,,Barry Simon,Barry (Princeton University Simon, New Jersey)**Publisher:**Gulf Professional Publishing**ISBN:**0125850506**Category:**Science**Page:**400**View:**4146

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.

## Elements of Functional Analysis

**Author**: I. J. Maddox**Publisher:**CUP Archive**ISBN:**9780521358682**Category:**Mathematics**Page:**242**View:**2390

This 1970 textbook aims to provide a truly introductory course in functional analysis.