Functional Analysis

Name: Functional Analysis
Brand: Dover Publications
Price: 33.99 EUR
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Frigyes Riesz Bela Sz. -Nagy(Autor*in)

Dover Publications (Verlag)

Erschienen am 27. Dezember 2012

1046 Seiten

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978-0-486-16214-0 (ISBN)

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Inhalt

Intro
Title Page
Copyright Page
PREFACE TO THE FIRST EDITION
PREFACE TO THE SECOND EDITION
Table of Contents
PART ONE - MODERN THEORIES OF DIFFERENTIATION AND INTEGRATION
CHAPTER I - DIFFERENTIATION
LEBESGUE'S THEOREM ON THE DERIVATIVE OF A MONOTONIC FUNCTION
SOME IMMEDIATE CONSEQUENCES OF LEBESGUE'S THEOREM
INTERVAL FUNCTIONS
CHAPTER II - THE LEBESGUE INTEGRAL
DEFINITION AND FUNDAMENTAL PROPERTIES
INDEFINITE INTEGRALS ABSOLUTELY CONTINUOUS FUNCTIONS
THE SPACE L2 AND ITS LINEAR FUNCTIONALS. Lp SPACES
FUNCTIONS OF SEVERAL VARIABLES
OTHER DEFINITIONS OF THE LEBESGUE INTEGRAL
CHAPTER III - THE STIELTJES INTEGRAL AND ITS GENERALIZATIONS
LINEAR FUNCTIONALS ON THE SPACE OF CONTINUOUS FUNCTIONS
GENERALIZATIONS OF THE STIELTJES INTEGRAL
THE DANIELL INTEGRAL
PART TWO - INTEGRAL EQUATIONS LINEAR TRANSFORMATIONS
CHAPTER IV - INTEGRAL EQUATIONS
THE METHOD OF SUCCESSIVE APPROXIMATIONS
THE FREDHOLM ALTERNATIVE
FREDHOLM DETERMINANTS
ANOTHER METHOD, BASED ON COMPLETE CONTINUITY
APPLICATIONS TO POTENTIAL THEORY
CHAPTER V - HILBERT AND BANACH SPACES
HILBERT SPACE
BANACH SPACES
CHAPTER VI - COMPLETELY CONTINUOUS SYMMETRIC TRANSFORMATIONS OF HILBERT SPACE
EXISTENCE OF CHARACTERISTIC ELEMENTS. THEOREM ON SERIES DEVELOPMENT
TRANSFORMATIONS WITH SYMMETRIC KERNEL
APPLICATIONS TO THE VIBRATING STRING PROBLEM AND TO ALMOST PERIODIC FUNCTIONS
CHAPTER VII - BOUNDED SYMMETRIC, UNITARY, AND NORMAL TRANSFORMATIONS OF HILBERT SPACE
SYMMETRIC TRANSFORMATIONS
UNITARY AND NORMAL TRANSFORMATIONS
UNITARY TRANSFORMATIONS OF THE SPACE L2
CHAPTER VIII - UNBOUNDED LINEAR TRANSFORMATIONS OF HILBERT SPACE
GENERALIZATION OF THE CONCEPT OF LINEAR TRANSFORMATION
SELF-ADJOINT TRANSFORMATIONS. SPECTRAL DECOMPOSITION
EXTENSIONS OF SYMMETRIC TRANSFORMATIONS
CHAPTER IX - SELF-ADJOINT TRANSFORMATIONS FUNCTIONAL CALCULUS, SPECTRUM, PERTURBATIONS
FUNCTIONAL CALCULUS
THE SPECTRUM OF A SELF-ADJOINT TRANSFORMATION AND ITS PERTURBATIONS
CHAPTER X - GROUPS AND SEMI-GROUPS OF TRANSFORMATIONS
UNITARY TRANSFORMATIONS
NON-UNITARY TRANSFORMATIONS
ERGODIC THEOREMS
CHAPTER XI - SPECTRAL THEORIES FOR LINEAR TRANSFORMATIONS OF GENERAL TYPE
APPLICATIONS OF METHODS FROM THE THEORY OF FUNCTIONS
VON NEUMANN'S THEORY OF SPECTRAL SETS
BIBLIOGRAPHY
APPENDIX - EXTENSIONS OF LINEAR TRANSFORMATIONS IN HILBERT SPACE WHICH EXTEND BEYOND THIS SPACE
SUPPLEMENTARY BIBLIOGRAPHY
INDEX
NOTATION AND SYMBOLS
A CATALOG OF SELECTED DOVER BOOKS IN ALL FIELDS OF INTEREST

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