Functional analysis: entering Hilbert space
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2016]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 176 Seiten Illustrationen, Diagramme |
| ISBN: | 9789814733922 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV043378402 | ||
| 003 | DE-604 | ||
| 005 | 20160713 | ||
| 007 | t | ||
| 008 | 160219s2016 xxua||| |||| 00||| eng d | ||
| 010 | |a 015038647 | ||
| 020 | |a 9789814733922 |9 978-981-4733-92-2 | ||
| 035 | |a (OCoLC)950430626 | ||
| 035 | |a (DE-599)BVBBV043378402 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-739 |a DE-91G |a DE-19 | ||
| 050 | 0 | |a QA320 | |
| 082 | 0 | |a 515/.733 |2 23 | |
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a MAT 463f |2 stub | ||
| 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, Technical University of Denmark, Denmark |
| 250 | |a Second edition | ||
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xvi, 176 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 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 Lp-Raum |0 (DE-588)4168195-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |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 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028797154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028797154 | ||
Record in the Search Index
| _version_ | 1804175943337508864 |
|---|---|
| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
Preliminary Notions xi
1. Basic Elements of Metric Topology 1
1.1 Metric spaces................................................ 1
1.2 The topology of a metric space............................... 5
1.3 Completeness and compactness of metric spaces................ 7
1.4 The Banach Fixed Point Theorem.............................. 11
1.5 The Baire Category Theorem.................................. 13
1.6 Normed vector spaces........................................ 15
1.7 Bounded linear operators.................................... 17
1.8 The Open Mapping Theorem.................................... 21
1.9 The Hahn-Banach Theorem..................................... 24
2. New Types of Function Spaces 29
2.1 Completion of metric spaces and normed vector spaces........ 29
2.2 The Weierstrass Approximation Theorem....................... 34
2.3 Important inequalities for p֊norms in spaces of continuous
functions .................................................. 38
2.4 Construction of Lp-spaces................................... 42
2.4.1 The Lp֊spaces and some basic inequalities .......... 42
2.4.2 Lebesgue measurable subsets in M.................... 45
2.4.3 Smooth functions with compact support................ 48
XV
xvi Functional Analysis: Entering Hilbert Space
2.4.4 Riemann integrable functions.............................. 49
2.5 The sequence spaces lp........................................ 51
3. Theory of Hilbert Spaces 55
3.1 Inner product spaces............................................ 55
3.2 Hilbert spaces.................................................. 60
3.3 Basis in a normed vector space and separability............... 61
3.3.1 Infinite series in normed vector spaces................. 61
3.3.2 Separability of a normed vector space................... 62
3.4 Basis in a separable Hilbert space............................ 64
3.5 Orthogonal projection and complement ........................... 72
3.6 Weak convergence................................................ 77
4. Operators on Hilbert Spaces 81
4.1 The adjoint of a bounded linear operator ..................... 81
4.2 Compact operators............................................... 88
5. Spectral Theory 95
5.1 The spectrum and the resolvent................................ 95
5.2 Spectral theorem for compact self-adjoint operators............. 99
6. Fredholm Theory 107
6.1 Dual spaces and operators.......................................107
6.2 A duality theorem for operators with closed image................113
6.3 Fredholm Operators..............................................118
6.4 Topology of spaces of operators.................................126
6.5 Integral operators and integral equations.......................132
6.6 Operator equations of Fredholm Type.............................137
Exercises 141
Bibliography . 169
List of Symbols 171
Index
173
|
| any_adam_object | 1 |
| author | Hansen, Vagn Lundsgaard 1940- |
| author_GND | (DE-588)111335299 |
| author_facet | Hansen, Vagn Lundsgaard 1940- |
| author_role | aut |
| author_sort | Hansen, Vagn Lundsgaard 1940- |
| author_variant | v l h vl vlh |
| building | Verbundindex |
| bvnumber | BV043378402 |
| callnumber-first | Q - Science |
| callnumber-label | QA320 |
| callnumber-raw | QA320 |
| callnumber-search | QA320 |
| callnumber-sort | QA 3320 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| classification_tum | MAT 463f |
| ctrlnum | (OCoLC)950430626 (DE-599)BVBBV043378402 |
| dewey-full | 515/.733 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.733 |
| dewey-search | 515/.733 |
| dewey-sort | 3515 3733 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01868nam a2200469 c 4500</leader><controlfield tag="001">BV043378402</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160713 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">160219s2016 xxua||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">015038647</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814733922</subfield><subfield code="9">978-981-4733-92-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)950430626</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043378402</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA320</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.733</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 463f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hansen, Vagn Lundsgaard</subfield><subfield code="d">1940-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)111335299</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Functional analysis</subfield><subfield code="b">entering Hilbert space</subfield><subfield code="c">Vagn Lundsgaard Hansen, Technical University of Denmark, Denmark</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo</subfield><subfield code="b">World Scientific</subfield><subfield code="c">[2016]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2016</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xvi, 176 Seiten</subfield><subfield code="b">Illustrationen, Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hilbert space</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hilbert-Raum</subfield><subfield code="0">(DE-588)4159850-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lp-Raum</subfield><subfield code="0">(DE-588)4168195-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Hilbert-Raum</subfield><subfield code="0">(DE-588)4159850-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Lp-Raum</subfield><subfield code="0">(DE-588)4168195-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028797154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028797154</subfield></datafield></record></collection> |
| id | DE-604.BV043378402 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:24:19Z |
| institution | BVB |
| isbn | 9789814733922 |
| language | English |
| lccn | 015038647 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028797154 |
| oclc_num | 950430626 |
| open_access_boolean | |
| owner | DE-739 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| owner_facet | DE-739 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | xvi, 176 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Hansen, Vagn Lundsgaard 1940- Verfasser (DE-588)111335299 aut Functional analysis entering Hilbert space Vagn Lundsgaard Hansen, Technical University of Denmark, Denmark Second edition New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2016] © 2016 xvi, 176 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Lp-Raum (DE-588)4168195-2 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 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=028797154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hansen, Vagn Lundsgaard 1940- Functional analysis entering Hilbert space Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Lp-Raum (DE-588)4168195-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4168195-2 (DE-588)4018916-8 |
| title | Functional analysis entering Hilbert space |
| title_auth | Functional analysis entering Hilbert space |
| title_exact_search | Functional analysis entering Hilbert space |
| title_full | Functional analysis entering Hilbert space Vagn Lundsgaard Hansen, Technical University of Denmark, Denmark |
| title_fullStr | Functional analysis entering Hilbert space Vagn Lundsgaard Hansen, Technical University of Denmark, Denmark |
| title_full_unstemmed | Functional analysis entering Hilbert space Vagn Lundsgaard Hansen, Technical University of Denmark, Denmark |
| title_short | Functional analysis |
| title_sort | functional analysis entering hilbert space |
| title_sub | entering Hilbert space |
| topic | Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Lp-Raum (DE-588)4168195-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Hilbert space Hilbert-Raum Lp-Raum Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028797154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hansenvagnlundsgaard functionalanalysisenteringhilbertspace |