Introductory functional analysis with applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Wiley
1989
|
| Series: | Wiley classics library
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 688 S. Ill., graph. Darst. |
| ISBN: | 0471504599 9780471504597 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introductory functional analysis with applications |c Erwin Kreyszig |
| 264 | 1 | |a New York |b Wiley |c 1989 | |
| 300 | |a XIV, 688 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804126224054747136 |
|---|---|
| adam_text | CONTENTS
Chapter
1.
Metric Spaces
1.1
Metric Space
2
1.2
Further Examples of Metric Spaces
9
1.3
Open Set, Closed Set, Neighborhood
17
1.4
Convergence, Cauchy Sequence, Completeness
25
1.5
Examples. Completeness Proofs
32
1.6
Completion of Metric Spaces
41
Chapter
2.
Normed Spaces. Banach Spaces
.....49
2.1
Vector Space
50
2.2
Normed Space. Banach Space
58
2.3
Further Properties of Normed Spaces
67
2.4
Finite Dimensional Normed Spaces and Subspaces
72
2.5
Compactness and Finite Dimension
77
2.6
Linear Operators
82
2.7
Bounded and Continuous Linear Operators
91
2.8
Linear Functionals
103
2.9
Linear Operators and Functionals on Finite Dimen¬
sional Spaces 111
2.10
Normed Spaces of Operators. Dual Space
117
Chapters. Inner Product Spaces. Hilbert Spaces.
. .127
3.1
Inner Product Space. Hilbert Space
128
3.2
Further Properties of Inner Product Spaces
136
3.3
Orthogonal Complements and Direct Sums
142
3.4
Orthonormal
Sets and Sequences
151
3.5
Series Related to
Orthonormal
Sequences and Sets
160
3.6
Total
Orthonormal
Sets and Sequences
167
3.7
Legendre,
Hermité
and Laguerre Polynomials
175
3.8
Representation of Functionals on Hilbert Spaces
188
3.9
Hilbert-Adjoint Operator
195
3.10
Self-Adjoint, Unitary and Normal Operators
201
Contents
Chapter
4. Fundamental Theorems
for Normed
and Banach Spaces...........209
4.1 Zorn s Lemma 210
4.2 Hahn-Banach Theorem 213
4.3 Hahn-Banach Theorem
for Complex Vector
Spaces
and
Normed Spaces 218
4.4 Application
to Bounded
Linear
Functionals on
C[a,
b]
225
4.5
Adjoint Operator
231
4.6
Reflexive Spaces
239
4.7
Category Theorem. Uniform Boundedness Theorem
246
4.8
Strong and Weak Convergence
256
4.9
Convergence of Sequences of Operators and
Functionals
263
4.10
Application to Summability of Sequences
269
4.11
Numerical Integration and Weak* Convergence
276
4.12
Open Mapping Theorem
285
4.13
Closed Linear Operators. Closed Graph Theorem
291
Chapter
5.
Further Applications: Banach Fixed
Point Theorem
............299
5.1
Banach Fixed Point Theorem
299
5.2
Application of Banach s Theorem to Linear Equations
307
5.3
Applications of Banach s Theorem to Differential
Equations
314
5.4
Application of Banach s Theorem to Integral
Equations
319
Chapter
6.
Further Applications: Approximation
Theory
...............327
6.1
Approximation in Normed Spaces
327
6.2
Uniqueness, Strict Convexity
330
6.3
Uniform Approximation
336
6.4
Chebyshev Polynomials
345
6.5
Approximation in Hubert Space
352
6.6
Splines
356
Chapter
7.
Spectral Theory of Linear Operators
in Normed Spaces
...........363
7.1
Spectral Theory in Finite Dimensional Normed Spaces
364
7.2
Basic Concepts
370
Contents
χι
7.3
Spectral
Properties of Bounded Linear Operators
374
7.4
Further Properties of Resolvent and Spectrum
379
7.5
Use of Complex Analysis in Spectral Theory
386
7.6
Banach Algebras
394
7.7
Further Properties of Banach Algebras
398
Chapter
8.
Compact Linear Operators on Normed
Spaces and Their Spectrum
......405
8.1
Compact Linear Operators on Normed Spaces
405
8.2
Further Properties of Compact Linear Operators
412
8.3
Spectral Properties of Compact Linear Operators on
Normed Spaces
419
8.4
Further Spectral Properties of Compact Linear
Operators
428
8.5
Operator Equations Involving Compact Linear
Operators
436
8.6
Further Theorems of
Fredholm
Type
442
8.7
Fredholm
Alternative
451
Chapter
9.
Spectral Theory of Bounded
Selí-
Adjoint Linear Operators
.....459
9.1
Spectral Properties of Bounded Self-Adjoint Linear
Operators
460
9.2
Further Spectral Properties of Bounded Self-Ad joint
Linear Operators
465
9.3
Positive Operators
469
9.4
Square Roots of a Positive Operator
476
9.5
Projection Operators
480
9.6
Further Properties of Projections
486
9.7
Spectral Family
492
9.8
Spectral Family of a Bounded Self-Adjoint Linear
Operator
497
9.9
Spectral Representation of Bounded Self-Adjoint Linear
Operators
505
9.10
Extension of the Spectral Theorem to Continuous
Functions
512
9.11
Properties of the Spectral Family of a Bounded Self-
Adjoint Linear Operator
516
xii Contents
Chapter
10.
Unbounded Linear Operators in
Hubert Space
............523
10.1
Unbounded Linear Operators and their
Hilbert-Adjoint Operators
524
10.2
Hilbert-Adjoint Operators, Symmetric and Self-Adjoint
Linear Operators
530
10.3
Closed Linear Operators and Closures
535
10.4
Spectral Properties of Self-Adjoint Linear Operators
541
10.5
Spectral Representation of Unitary Operators
546
10.6
Spectral Representation of Self-Adjoint Linear Operators
556
10.7
Multiplication Operator and Differentiation Operator
562
Chapter
11.
Unbounded Linear Operators in
Quantum Mechanics
.........571
11.1
Basic Ideas. States,
Observables,
Position Operator
572
11.2
Momentum Operator.
Heisenberg
Uncertainty Principle
576
11.3
Time-Independent
Schrödinger
Equation
583
11.4
Hamilton Operator
590
11.5
Time-Dependent
Schrödinger
Equation
598
Appendix
1.
Some Material for Review and
Reference
..............609
A
1.1
Sets
609
A
1.2
Mappings
613
A1.3 Families
617
A
1.4
Equivalence Relations
618
Al.
5
Compactness
618
Al.
6
Supremum and Infimum
619
Al.
7
Cauchy Convergence Criterion
620
A
1.8
Groups
622
Appendix
2.
Answers to Odd-Numbered Problems
. 623
Appendix
3.
References
..............675
Index
.......................681
|
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| indexdate | 2024-07-09T18:14:03Z |
| institution | BVB |
| isbn | 0471504599 9780471504597 |
| language | English |
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| physical | XIV, 688 S. Ill., graph. Darst. |
| publishDate | 1989 |
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| publisher | Wiley |
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| series2 | Wiley classics library |
| spelling | Kreyszig, Erwin 1922-2008 Verfasser (DE-588)117714518 aut Introductory functional analysis with applications Erwin Kreyszig New York Wiley 1989 XIV, 688 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley classics library Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007880146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kreyszig, Erwin 1922-2008 Introductory functional analysis with applications Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4151278-9 |
| title | Introductory functional analysis with applications |
| title_auth | Introductory functional analysis with applications |
| title_exact_search | Introductory functional analysis with applications |
| title_full | Introductory functional analysis with applications Erwin Kreyszig |
| title_fullStr | Introductory functional analysis with applications Erwin Kreyszig |
| title_full_unstemmed | Introductory functional analysis with applications Erwin Kreyszig |
| title_short | Introductory functional analysis with applications |
| title_sort | introductory functional analysis with applications |
| topic | Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Funktionalanalysis Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007880146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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