Functional analysis: a terse introduction
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
2017
|
| Series: | De Gruyter Graduate
|
| Subjects: | |
| Online Access: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110441918&searchTitles=true Inhaltsverzeichnis |
| Physical Description: | XIII, 227 Seiten Diagramme |
| ISBN: | 9783110441918 3110441918 |
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MARC
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| 100 | 1 | |a Chacón, Gerardo |d 1979- |e Verfasser |0 (DE-588)1123305889 |4 aut | |
| 245 | 1 | 0 | |a Functional analysis |b a terse introduction |c Gerardo R. Chacón, Humberto Rafeiro, Juan C. Vallejo |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c 2017 | |
| 264 | 4 | |c © 2017 | |
| 300 | |a XIII, 227 Seiten |b Diagramme | ||
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| 700 | 1 | |a Vallejo, Juan Camilo |e Verfasser |0 (DE-588)1128498200 |4 aut | |
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Record in the Search Index
| _version_ | 1804176737406287872 |
|---|---|
| adam_text | XV
Con
l ist i i i ;
B¿isi* i!-‘
----XVII
--1
Axiom of Choice---1
Some Applications----3
Problems---6
----8
2.1 Norms-----8
2.2 Inner Products and Hilbert Spaces--14
2.3 Some Geometric Properties-----20
2.4 Orthogonality----24
2.5 Orthogonal Sequences-----27
2.6 Problems-----34
; ----36
3.1 Banach Spaces------36
3.2 Completion and Dimension------43
3.3 Separability---45
3.4 Problems-----52
i
1.1
1.2
1.3
----53
4.1 Linear Transformations--53
4.2 Back to Matrices--54
4.3 Boundedness-----57
4.4 Problems----64
---66
5.1 A Special Type of Linear Operators-66
5.2 Dual Spaces---69
5-3 The Bra-ket Notation-73
5.4 Problems----76
---78
The Space L2[-n, n]---78
Convergence Conditions for the Fourier Sériés-80
XII
6.2.1
6.2.2
6.3
7.1
7.2
7.3
7.4
7.5
8.1
8.1.1
8.1.2
8.1.3
8.1.4
8.2
9.1
9.2
9.3
10.1
11.1
12.1
13.1
13.2
13.3
13.4
13.5
Contents
Sufficient Convergence Conditions for the Fourier Series in
a Point---80
Conditions for Uniform Convergence for the Fourier
Series---84
Problems----87
----89
Convolution----89
L1 Theory----94
L2 Theory---105
Schwartz Class----108
Problems----111
---113
Some Applications----116
Neumann Series-----116
Differential Equations--117
Integral Equations---118
Fractals---119
Problems----124
---126
Baire Categories---126
Baire Category Theorem----127
Problems----135
---137
Problems----142
---143
Problems----146
---147
Problems----149
---151
Extension Theorems----151
Minkowski Functional----155
Separation Theorem----158
Applications of the Hahn-Banach Theorem----163
Problems----165
Contents
XIII
14.1
14.2
14.3
15.1
15.2
15.3
16.1
16.2
16.3
17.1
17.2
17.3
18.1
18.2
18.2.1
18.2.2
18.2.3
18.3
---166
Hilbert Spaces---166
Banach Spaces----170
Problems----172
----174
Weak* Topology-----177
Reflexive Spaces---179
Problems-----182
---183
Compact Operators-----183
Normal and Self-Adjoint Operators---187
Problems-----190
----192
A Quick Review of Spectral Theory in Finite Dimensions-192
The Spectral Theorem for Compact Self-Adjoint Operators-194
Problems----197
---199
Metric Spaces---199
Compactness in Some Function Spaces---209
Space e2---209
Space of Continuous Functions--211
Lebesgue Spaces----216
Problems----221
225
223
|
| any_adam_object | 1 |
| author | Chacón, Gerardo 1979- Rafeiro, Humberto Vallejo, Juan Camilo |
| author_GND | (DE-588)1123305889 (DE-588)1102903299 (DE-588)1128498200 |
| author_facet | Chacón, Gerardo 1979- Rafeiro, Humberto Vallejo, Juan Camilo |
| author_role | aut aut aut |
| author_sort | Chacón, Gerardo 1979- |
| author_variant | g c gc h r hr j c v jc jcv |
| building | Verbundindex |
| bvnumber | BV043858695 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)969670573 (DE-599)DNB1076283683 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043858695 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:36:56Z |
| institution | BVB |
| isbn | 9783110441918 3110441918 |
| language | English |
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| physical | XIII, 227 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Graduate |
| spelling | Chacón, Gerardo 1979- Verfasser (DE-588)1123305889 aut Functional analysis a terse introduction Gerardo R. Chacón, Humberto Rafeiro, Juan C. Vallejo Berlin ; Boston De Gruyter 2017 © 2017 XIII, 227 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Fachhochschul-/Hochschulausbildung Funktionalanalysis (DE-588)4018916-8 s DE-604 Rafeiro, Humberto Verfasser (DE-588)1102903299 aut Vallejo, Juan Camilo Verfasser (DE-588)1128498200 aut Erscheint auch als Online-Ausgabe, EPUB 978-3-11-043364-7 Erscheint auch als Online-Ausgabe, PDF 978-3-11-044192-5 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110441918&searchTitles=true Verlag 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=029268855&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chacón, Gerardo 1979- Rafeiro, Humberto Vallejo, Juan Camilo Functional analysis a terse introduction Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Functional analysis a terse introduction |
| title_auth | Functional analysis a terse introduction |
| title_exact_search | Functional analysis a terse introduction |
| title_full | Functional analysis a terse introduction Gerardo R. Chacón, Humberto Rafeiro, Juan C. Vallejo |
| title_fullStr | Functional analysis a terse introduction Gerardo R. Chacón, Humberto Rafeiro, Juan C. Vallejo |
| title_full_unstemmed | Functional analysis a terse introduction Gerardo R. Chacón, Humberto Rafeiro, Juan C. Vallejo |
| title_short | Functional analysis |
| title_sort | functional analysis a terse introduction |
| title_sub | a terse introduction |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110441918&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029268855&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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