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ELEMENTS OF FUNCTIONAL ANALYSIS (GRADUATE TEXTS IN By Francis Hirsch & Gilles
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Item specifics
- Condition
- ISBN-10
- 0387985247
- Book Title
- Elements of Functional Analysis (Graduate Texts in Mathematics)
- ISBN
- 9780387985244
About this product
Product Identifiers
Publisher
Springer New York
ISBN-10
0387985247
ISBN-13
9780387985244
eBay Product ID (ePID)
870084
Product Key Features
Number of Pages
Xiv, 396 Pages
Publication Name
Elements of Functional Analysis
Language
English
Subject
Functional Analysis, Mathematical Analysis
Publication Year
1999
Type
Textbook
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
0.4 in
Item Weight
59.6 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
98-053153
Dewey Edition
21
Series Volume Number
192
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515.7
Table Of Content
Prologue: Sequences.- 1 Countability.- 2 Separability.- 3 The Diagonal Procedure.- 4 Bounded Sequences of Continuous Linear Maps.- I Function Spaces and Their Duals.- 1 The Space of Continuous Functions on a Compact Set.- 1 Generalities.- 2 The Stone--Weierstrass Theorems.- 3 Ascoli's Theorem.- 2 Locally Compact Spaces and Radon Measures.- 1 Locally Compact Spaces.- 2 Daniell's Theorem.- 3 Positive Radon Measures.- 3A Positive Radon Measures on $${{\mathbb{R}}^{d}}$$ and the Stieltjes Integral.- 3B Surface Measure on Spheres in $${{\mathbb{R}}^{d}}$$.- 4 Real and Complex Radon Measures.- 3 Hilbert Spaces.- 1 Definitions, Elementary Properties, Examples.- 2 The Projection Theorem.- 3 The Riesz Representation Theorem.- 3A Continuous Linear Operators on a Hilbert Space.- 3B Weak Convergence in a Hilbert Space.- 4 Hilbert Bases.- 4 LpSpaces.- 1 Definitions and General Properties.- 2 Duality.- 3 Convolution.- II Operators.- 5 Spectra.- 1 Operators on Banach Spaces.- 2 Operators in Hilbert Spaces.- 2A Spectral Properties of Hermitian Operators.- 2B Operational Calculus on Hermitian Operators.- 6 Compact Operators.- 1 General Properties.- lA Spectral Properties of Compact Operators.- 2 Compact Selfadjoint Operators.- 2A Operational Calculus and the Fredholm Equation.- 2B Kernel Operators.- III Distributions.- 7 Definitions and Examples.- 1 Test Functions.- lA Notation.- 1B Convergence in Function Spaces.- 1C Smoothing.- 1D C?Partitions of Unity.- 2 Distributions.- 2A Definitions.- 2B First Examples.- 2C Restriction and Extension of a Distribution to an Open Set.- 2D Convergence of Sequences of Distributions.- 2E Principal Values.- 2F Finite Parts.- 3 Complements.- 3A Distributions of Finite Order.- 3B The Support of a Distribution.- 3C Distributions with Compact Support.- 8 Multiplication and Differentiation.- 1 Multiplication.- 2 Differentiation.- 3 Fundamental Solutions of a Differential Operator.- 3A The Laplacian.- 3B The Heat Operator.- 3C The Cauchy-Riemann Operator.- 9 Convolution of Distributions.- 1 Tensor Product of Distributions.- 2 Convolution of Distributions.- 2A Convolution in ?'.- 2B Convolution in D'.- 2C Convolution of a Distribution with a Function.- 3 Applications.- 3A Primitives and Sobolev's Theorem.- 3B Regularity.- 3C Fundamental Solutions and Partial Differential Equations.- 3D The Algebra D+'.- 10 The Laplacian on an Open Set.- 1 The spaces H1(?) and H01(?).- 2 The Dirichlet Problem.- 2A The Dirichlet Problem.- 2B The Heat Problem.- 2C The Wave Problem.- Answers to the Exercises.
Synopsis
This book arose from a course taught for several years at the Univer- sity of Evry-Val d'Essonne. It is meant primarily for graduate students in mathematics. To make it into a useful tool, appropriate to their knowl- edge level, prerequisites have been reduced to a minimum: essentially, basic concepts of topology of metric spaces and in particular of normed spaces (convergence of sequences, continuity, compactness, completeness), of "ab- stract" integration theory with respect to a measure (especially Lebesgue measure), and of differential calculus in several variables. The book may also help more advanced students and researchers perfect their knowledge of certain topics. The index and the relative independence of the chapters should make this type of usage easy. The important role played by exercises is one of the distinguishing fea- tures of this work. The exercises are very numerous and written in detail, with hints that should allow the reader to overcome any difficulty. Answers that do not appear in the statements are collected at the end of the volume. There are also many simple application exercises to test the reader's understanding of the text, and exercises containing examples and coun- terexamples, applications of the main results from the text, or digressions to introduce new concepts and present important applications. Thus the text and the exercises are intimately connected and complement each other., This book presents the fundamental function spaces and their duals, explores operator theory and finally develops the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Includes an assortment of well formulated exercises, with answers and hints collected at the end of the book., This book arose from a course taught for several years at the Univer sity of Evry-Val d'Essonne. It is meant primarily for graduate students in mathematics. To make it into a useful tool, appropriate to their knowl edge level, prerequisites have been reduced to a minimum: essentially, basic concepts of topology of metric spaces and in particular of normed spaces (convergence of sequences, continuity, compactness, completeness), of "ab stract" integration theory with respect to a measure (especially Lebesgue measure), and of differential calculus in several variables. The book may also help more advanced students and researchers perfect their knowledge of certain topics. The index and the relative independence of the chapters should make this type of usage easy. The important role played by exercises is one of the distinguishing fea tures of this work. The exercises are very numerous and written in detail, with hints that should allow the reader to overcome any difficulty. Answers that do not appear in the statements are collected at the end of the volume. There are also many simple application exercises to test the reader's understanding of the text, and exercises containing examples and coun terexamples, applications of the main results from the text, or digressions to introduce new concepts and present important applications. Thus the text and the exercises are intimately connected and complement each other.
LC Classification Number
QA1-939
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