Functional Analysistxt,chm,pdf,epub,mobi下载 作者:Dzung Minh Ha 出版社: Matrix Editions 副标题: Volume I: A Gentle Introduction 出版年: 2006-6 页数: 640 定价: USD 68.00 装帧: Hardcover ISBN: 9780971576612 内容简介 · · · · · ·From the preface: This book is designed as an introduction to basic functional analysis at the senior/graduate level. It has been written in such a way that a well-motivated undergraduate student can follow and appreciate the material without undue difficulties while an advanced graduate student can also find topics of interest: topological vector spaces, Kolmogorov's normabili... 目录 · · · · · ·Chapter 0: three important inequalities 1Chapter 1: Metric and topological spaces 6 1.1 Metrics and metric spaces 1.2 Open and closed sets 1.3 Topological spaces 1.4 Continuous functions · · · · · ·() Chapter 0: three important inequalities 1 Chapter 1: Metric and topological spaces 6 1.1 Metrics and metric spaces 1.2 Open and closed sets 1.3 Topological spaces 1.4 Continuous functions 1.5 Open sets and continuity 1.6 Some important topological concepts 1.7 Convergence of sequences in metric spaces 1.8 Completeness 1.9 Density, separability, and approximation 1.10 Metric space completions 1.11 Compactness 1.12 The Banach fixed point theorem 1.13 Baire's category theorem Chapter 2: Normed spaces 116 2.1 Linear operators on function spaces 2.2 Hamel bases 2.3 Norms and normed spaces 2.4 Topological concepts in normed spaces 2.5 Topological vector spaces 2.6 Kolmogorov's theorem 2.7 Banach spaces 2.8 Infinite series in normed spaces 2.9 Schauder bases 2.10 Linear functionals and hyperplanes 2.11 Constructing new normed spaces Chapter 3: Operators on normed spaces 206 3.1 Continuous linear maps 3.2 Integral operators 3.3 Linear homeomorphisms 3.4 Three important theorems 3.5 The normed space B(X,Y) 3.6 Complementary subspaces and projections 3.7 Riesz's lemma 3.8 The spectrum of a bounded linear operator 3.9 Continuous linear functionals and dual spaces Chapter 4: Inner product spaces 291 4.1 Definitions and examples 4.2 Orthogonality 4.3 Unitary isomorphisms 4.4 Inner product spaces: three problems 4.5 Three characterizations for Hilbert spaces 4.6 Hilbert bases Chapter 5: The Banach space C(X) 365 5.1 The Arzela-Ascoli theorem 5.2 Korovkin's theorem and the Weierstrass approximation theorem 5.3 Sub-algebras 5.4 The Stone-Weierstrass theorem Chapter 6: Additional topics 415 6.1 The Baire-Osgood theorem 6.2 Gram determinants and Muntz's theorem 6.3 Differential equations Appendix A: Set theory and functions 464 A.1 Sets A.2 Relations A.3 Zorn's lemma and the axiom of choice A.4 Functions A.5 Cardinality A.6 The axiom of completeness on R Appendix B: Mostly linear algebra (a brief review) 480 B.1 Polynomials and sequences B.2 Vector spaces B.3 Linear independence and span B.4 Bases and dimension B.5 Linear transformations B.6 Partial derivatives and the mean value theorem B.7 Riemann integrals Appendix C: Some technical results 491 Appendix D: Solutions to odd-numbered exercises 494 Bibliography 618 Notation 622 Index 624 · · · · · · () |
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