Functional Analysis

Peter D. Lax

580 pages, parution le 30/04/2002

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Résumé

Offers graduate level coverage of functional analysis, including standard topics such as topology, linear operators, and Gelfand's theory of commutative Banach algebras. Problems and exercises are included.

Contents

Foreword

1 Linear Spaces 1
2 Linear Maps 8
3 The Hahn-Banach Theorem 19
4 Applications of the Hahn-Banach theorem 29
5 Normed Linear spaces 36
6 Hilbert Space 52
7 Applications of Hilbert Space Results 63
8 Duals of Normed Linear Spaces 72
9 Applications of Duality 87
10 Weak Convergence 99
11 Applications of Weak Convergence 108
12 The Weak and Weak[superscript *] Topologies 118
13 Locally Convex Topologies and the Krein-Milman Theorem 122
14 Examples of Convex Sets and Their Extreme Points 133
15 Bounded Linear Maps 160
16 Examples of Bounded Linear Maps 173
17 Banach Algebras and their Elementary Spectral Theory 192
18 Gelfand's Theory of Commutative Banach Algebras 202
19 Applications of Gelfand's Theory of Commutative Banach Algebras 210
20 Examples of Operators and Their Spectra 226
21 Compact Maps 233
22 Examples of Compact Operators 245
23 Positive compact operators 253
24 Fredholm's Theory of Integral Equations 260
25 Invariant Subspaces 275
26 Harmonic Analysis on a Halfline 284
27 Index Theory 300
28 Compact Symmetric Operators in Hilbert Space 315
29 Examples of Compact Symmetric Operators 323
30 Trace Class and Trace Formula 329
31 Spectral Theory of Symmetric, Normal, and Unitary Operators 354
32 Spectral Theory of Self-Adjoint Operators 377
33 Examples of Self-Adjoint Operators 394
34 Semigroups of Operators 416
35 Groups of Unitary Operators 440
36 Examples of Strongly Continuous Semigroups 461
37 Scattering Theory 477
38 A Theorem of Beurling 513

A Riesz-Kakutani representation theorem 529
B Theory of distributions 543
C Zorn's Lemma 571

Author Index 573
Subject Index 577

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Peter D. Lax
Parution	30/04/2002
Nb. de pages	580
Format	16 x 24
Couverture	Relié
Poids	961g
Intérieur	Noir et Blanc
EAN13	9780471556046
ISBN13	978-0-471-55604-6