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Linear Functional Analysis

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Linear Functional Analysis

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Author : Bryan P. Rynne
language : en
Publisher: Springer Science & Business Media
Release Date : 2000

Linear Functional Analysis written by Bryan P. Rynne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further highlights of the second edition include: a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book.

Linear Functional Analysis

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Author : Bryan Rynne
language : en
Publisher:
Release Date : 2014-01-15

Linear Functional Analysis written by Bryan Rynne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Functional Analysis I

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Author : Yu.I. Lyubich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Functional Analysis I written by Yu.I. Lyubich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Up to a certain time the attention of mathematicians was concentrated on the study of individual objects, for example, specific elementary functions or curves defined by special equations. With the creation of the method of Fourier series, which allowed mathematicians to work with 'arbitrary' functions, the individual approach was replaced by the 'class' approach, in which a particular function is considered only as an element of some 'function space'. More or less simultane ously the development of geometry and algebra led to the general concept of a linear space, while in analysis the basic forms of convergence for series of functions were identified: uniform, mean square, pointwise and so on. It turns out, moreover, that a specific type of convergence is associated with each linear function space, for example, uniform convergence in the case of the space of continuous functions on a closed interval. It was only comparatively recently that in this connection the general idea of a linear topological space (L TS)l was formed; here the algebraic structure is compatible with the topological structure in the sense that the basic operations (addition and multiplication by a scalar) are continuous.

Linear Functional Analysis

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Author : Bryan Rynne
language : en
Publisher: Springer
Release Date : 2007-12-21

Linear Functional Analysis written by Bryan Rynne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-21 with Mathematics categories.

Linear Functional Analysis

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Author : Joan Cerda
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Linear Functional Analysis written by Joan Cerda and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. It avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems. The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology.

Linear Functional Analysis

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Author : Bryan Rynne
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-29

Linear Functional Analysis written by Bryan Rynne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-29 with Mathematics categories.

Linear And Nonlinear Functional Analysis With Applications

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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2013-10-10

Linear And Nonlinear Functional Analysis With Applications written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-10 with Mathematics categories.

This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.

Basic Methods Of Linear Functional Analysis

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Author : John Derwent Pryce
language : en
Publisher:
Release Date : 1973

Basic Methods Of Linear Functional Analysis written by John Derwent Pryce and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Functional analysis categories.

Functional Analysis I

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Author : Yu.I. Lyubich
language : en
Publisher: Springer
Release Date : 1992-02-06

Functional Analysis I written by Yu.I. Lyubich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-06 with Mathematics categories.

The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.

Functional Analysis And Control Theory

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Author : Stefan Rolewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-10-31

Functional Analysis And Control Theory written by Stefan Rolewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-10-31 with Mathematics categories.

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Linear Functional Analysis

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