Functional analysis: entering Hilbert space
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 136 S. graph. Darst. |
| ISBN: | 9812566864 9812565639 |
Internformat
MARC
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| 100 | 1 | |a Hansen, Vagn Lundsgaard |d 1940- |e Verfasser |0 (DE-588)111335299 |4 aut | |
| 245 | 1 | 0 | |a Functional analysis |b entering Hilbert space |c Vagn Lundsgaard Hansen |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2006 | |
| 300 | |a X, 136 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 4 | |a Análisis funcional | |
| 650 | 4 | |a Hilbert, Espace de | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Hilbert space | |
| 650 | 0 | 7 | |a Hilbert-Raum |0 (DE-588)4159850-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lp-Raum |0 (DE-588)4168195-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | 1 | |a Hilbert-Raum |0 (DE-588)4159850-7 |D s |
| 689 | 0 | 2 | |a Lp-Raum |0 (DE-588)4168195-2 |D s |
| 689 | 0 | |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-015024802 | ||
Datensatz im Suchindex
| _version_ | 1804135734075981824 |
|---|---|
| adam_text | Contents
Preface vii
Preliminary Notions
1
1.
Basic Elements of Metric Topology
5
1.1
Metric spaces
............................ 5
1.2
The topology of a metric space
.................. 9
1.3
Completeness of metric spaces
................... 11
1.4
Norrned vector spaces
....................... 15
1.5
Bounded linear operators
..................... 18
2.
New Types of Function Spaces
23
2.1
Completion of metric spaces and normed vector spaces
..... 23
2.2
The
Weierstrass
Approximation Theorem
............ 28
2.3
Important inequalities for j^-norms in spaces of continuous func¬
tions
................................. 32
2.4
Construction of L^-spaces
....................· 36
2.4.1
The // -spaces and some basic inequalities
........ 36
2.4.2
Lebesgue measurable subsets in
M
............. 39
2.4.3
Smooth functions with compact support
......... 42
2.4.4
Riemann
integrable
functions
............... 43
2.5
The sequence spaces lp
....................... 45
3.
Theory of Hubert Spaces
49
3.1
Inner product spaces
........................ 49
3.2
Hubert spaces
............................ 54
χ
Functional Analysis: Entering
Hubert
Space
3.3
Basis in a normed vector space and separability
......... 55
3.3.1
Infinite series in normed vector spaces
.......... 55
3.3.2
Separability of a normed vector space
........... 56
3.4
Basis in a separable Hubert space
................. 58
3.5
Orthogonal projection and complement
............. 66
3.6
Weak convergence
......................... 71
4.
Operators on Hubert Spaces
75
4.1
The adjoint of a bounded linear operator
............ 75
4.2
Compact operators
......................... 82
5.
Spectral Theory
89
5.1
The spectrum and the resolvent
.................. 89
5.2
Spectral theorem for compact self-adjoint operators
....... 93
Exercises
101
Bibliography
129
List of Symbols
131
Index
133
|
| adam_txt |
Contents
Preface vii
Preliminary Notions
1
1.
Basic Elements of Metric Topology
5
1.1
Metric spaces
. 5
1.2
The topology of a metric space
. 9
1.3
Completeness of metric spaces
. 11
1.4
Norrned vector spaces
. 15
1.5
Bounded linear operators
. 18
2.
New Types of Function Spaces
23
2.1
Completion of metric spaces and normed vector spaces
. 23
2.2
The
Weierstrass
Approximation Theorem
. 28
2.3
Important inequalities for j^-norms in spaces of continuous func¬
tions
. 32
2.4
Construction of L^-spaces
.· 36
2.4.1
The //"-spaces and some basic inequalities
. 36
2.4.2
Lebesgue measurable subsets in
M
. 39
2.4.3
Smooth functions with compact support
. 42
2.4.4
Riemann
integrable
functions
. 43
2.5
The sequence spaces lp
. 45
3.
Theory of Hubert Spaces
49
3.1
Inner product spaces
. 49
3.2
Hubert spaces
. 54
χ
Functional Analysis: Entering
Hubert
Space
3.3
Basis in a normed vector space and separability
. 55
3.3.1
Infinite series in normed vector spaces
. 55
3.3.2
Separability of a normed vector space
. 56
3.4
Basis in a separable Hubert space
. 58
3.5
Orthogonal projection and complement
. 66
3.6
Weak convergence
. 71
4.
Operators on Hubert Spaces
75
4.1
The adjoint of a bounded linear operator
. 75
4.2
Compact operators
. 82
5.
Spectral Theory
89
5.1
The spectrum and the resolvent
. 89
5.2
Spectral theorem for compact self-adjoint operators
. 93
Exercises
101
Bibliography
129
List of Symbols
131
Index
133 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV021812538 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:51:27Z |
| indexdate | 2024-07-09T20:45:12Z |
| institution | BVB |
| isbn | 9812566864 9812565639 |
| language | English |
| lccn | 2006045702 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015024802 |
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| physical | X, 136 S. graph. Darst. |
| publishDate | 2006 |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Hansen, Vagn Lundsgaard 1940- Verfasser (DE-588)111335299 aut Functional analysis entering Hilbert space Vagn Lundsgaard Hansen New Jersey [u.a.] World Scientific 2006 X, 136 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse fonctionnelle Análisis funcional Hilbert, Espace de Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Lp-Raum (DE-588)4168195-2 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s Hilbert-Raum (DE-588)4159850-7 s Lp-Raum (DE-588)4168195-2 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015024802&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hansen, Vagn Lundsgaard 1940- Functional analysis entering Hilbert space Analyse fonctionnelle Análisis funcional Hilbert, Espace de Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd Lp-Raum (DE-588)4168195-2 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4018916-8 (DE-588)4168195-2 |
| title | Functional analysis entering Hilbert space |
| title_auth | Functional analysis entering Hilbert space |
| title_exact_search | Functional analysis entering Hilbert space |
| title_exact_search_txtP | Functional analysis entering Hilbert space |
| title_full | Functional analysis entering Hilbert space Vagn Lundsgaard Hansen |
| title_fullStr | Functional analysis entering Hilbert space Vagn Lundsgaard Hansen |
| title_full_unstemmed | Functional analysis entering Hilbert space Vagn Lundsgaard Hansen |
| title_short | Functional analysis |
| title_sort | functional analysis entering hilbert space |
| title_sub | entering Hilbert space |
| topic | Analyse fonctionnelle Análisis funcional Hilbert, Espace de Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd Lp-Raum (DE-588)4168195-2 gnd |
| topic_facet | Analyse fonctionnelle Análisis funcional Hilbert, Espace de Functional analysis Hilbert space Hilbert-Raum Funktionalanalysis Lp-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015024802&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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