《Functional Analysis》电子书下载

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 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
· · · · · · ()
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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  1. neal0620 neal0620说道:
    1#

    生动有趣的诠释了

  2. 子由你 子由你说道:
    2#

    令我大开眼界

  3. 小君仔是我 小君仔是我说道:
    3#

    书很好,很值得

  4. 幽若小晶 幽若小晶说道:
    4#

    有思想

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