Bases in function spaces, sampling, discrepancy, numerical integration:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
[2010]
|
| Series: | EMS tracts in mathematics
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 296 Seiten Diagramme |
| ISBN: | 9783037190852 |
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MARC
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| 100 | 1 | |a Triebel, Hans |d 1936- |e Verfasser |0 (DE-588)133515923 |4 aut | |
| 245 | 1 | 0 | |a Bases in function spaces, sampling, discrepancy, numerical integration |c Hans Triebel |
| 264 | 1 | |a Zürich |b European Mathematical Society |c [2010] | |
| 264 | 4 | |c © 2010 | |
| 300 | |a IX, 296 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a EMS tracts in mathematics |v 11 | |
| 650 | 0 | 7 | |a Basis |g Mathematik |0 (DE-588)4228195-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerische Integration |0 (DE-588)4172168-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Basis |g Mathematik |0 (DE-588)4228195-7 |D s |
| 689 | 0 | 2 | |a Numerische Integration |0 (DE-588)4172168-8 |D s |
| 689 | 0 | |5 DE-604 | |
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| 830 | 0 | |a EMS tracts in mathematics |v 11 |w (DE-604)BV022480257 |9 11 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-021190682 | |
Record in the Search Index
| _version_ | 1811252338363465728 |
|---|---|
| adam_text |
Contents
Preface
v
1
Function spaces
1
1.1 Isotropie
spaces
.,.,.,,.,,. 1
1.1.1
Definitions
.
і
1.1.2
Atoms
. 4
1.1.3
Local means
. 6
1.1.4
Wavelets
. 8
1.1.5
Duality and interpolation
. 11
1.1.6
Spaces on domains
. 12
1.1.7
Limiting embeddings
. 16
1.1.8
Spaces of measurable functions
. 19
1.2
Spaces with dominating mixed smoothness
. 22
1.2.1
Definitions
. 22
1.2.2
Atoms
. 26
1.2.3
Local means
. 28
1.2.4
Wavelets
. 30
1.2.5
Higher dimensions
. 33
1.2.6
Spaces on domains:
definitionsproblems
. 35
1.2.7
Spaces on domains: representations, wavelets
. 36
1.2.8
Spaces on domains: extensions, intrinsic characterisations
. 44
1.3
Logarithmic spaces
. 50
1.3.1
Introduction
. 50
1.3.2
Logarithmic spaces on (R
. 52
1.3.3 Isotropie
logarithmic spaces: comments, problems, proposals
, 54
1.3.4
Logarithmic spaces with dominating mixed smoothness
. . 60
2 Haar
bases
63
2.1
Classical theory and historical comments
.,,.,.,,.,, 63
2.2 Haar
bases on
R
and on intervals
.,,.,.,,.,., 71
2.2.1
Introduction and plan of the chapter
.,,.,,,,.,.,., 71
2.2.2
Inequalities
. 72
2.2.3 Haar
bases on
R
.,.,,.,,. 80
2.2.4 Haar
bases on intervals
.,.,.,,.,.,. 84
2.2.5
Littlewood-Paley theorem
. 86
2.3 Haar
wavelet bases on R" and on cubes
. 88
2.3.1
Inequalities
. 88
2.3.2 Haar
wavelet bases on R"
. 92
2.3.3 Haar
wavelet bases on cubes
. 95
2.4 Haar
tensor bases on R" and on cubes
. 98
2.4.1
Introduction
. 98
2.4.2
Haar
tensor
bases on
R2,
1
. 99
2.4.3
Haar
tensor bases on
К2,
II
. 101
2.4.4
Haar
tensor bases on cubes
. 106
2.4.5
Higher dimensions
. 109
2.5
Spline bases
. 112
2.5.1
Preliminaries and basic assertions
. 112
2.5.2
Spline bases on
R
. 115
2.5.3
Spline wavelet bases on
R"
. 119
2.5.4
Spline tensor bases on
(R2
. 121
Faber bases
124
3.1
Faber bases on intervals
. 124
3.1.1
Introduction and preliminaries
. 124
3.1.2
Faber bases
. 126
3.1.3
Complements
. 130
3.2
Faber bases on cubes
. 133
3.2.1
Preliminaries and definitions
. 133
3.2.2
Faber bases in C^Q2)
. 135
3.2.3 FaberbasesinSJW'CCAandS^ßCQ2) . 138
3.2.4
The spaces S^qB(Q2) and S^H(Q2)
. 144
3.2.5
Higher dimensions
. 152
3.3
The spaces
Б^ЩП2)
. 154
3.3.1
Introduction and definition
. 154
3.3.2
Properties
. 157
3.4
Bases in logarithmic spaces
. 159
3.4.1
Preliminaries
. 159
3.4.2
The spaces Bp'g
(її)
and Bp'g (I)
. 160
3.4.3
The spaces Sp'qB(K2) and S'p'gB(Q2)
. 163
3.5
Faber splines: an outlook
. 165
3.5.1
Preparations
. 165
3.5.2
Faber splines
. 167
3.5.3
Comments, problems, proposals
. 172
Sampling
174
4.1
Definitions, sampling in
isotropie
spaces
. 174
4.1.1
Definitions
. 174
4.1.2
Sampling in
isotropie
spaces
. 176
4.1.3
Information uncertainty
. 181
4.2
Sampling on intervals
. 183
4.2.1
Sampling in Aspq(I)
. 183
4.2.2
Sampling in Aspq(I)
. 189
4.3
Sampling in spaces with dominating mixed smoothness
. 192
4.3.1
Introduction,
preliminaries
. 192
4.3.2
Main assertions
. . 195
4.3.3
Complements
. . 203
4.4
Sampling in logarithmic spaces with dominating mixed smoothness
. . 208
4.4.1
Introduction and motivation
. 208
4.4.2
Basic assertions
. 210
4.4.3
The spaces Spq
2?
(Q2), main assertions
.,,,, 212
4.4.4
Higher dimensions: comments, problems, proposals
. 215
5
Numerical integration
221
5.1
Preliminaries, integration in domains
. 221
5.1.1
Introduction, definitions
. 221
5.1.2
Integration in Lipschitz domains
. 223
5.1.3
A comment on integration in
£
-thick domains
. 224
5.2
Integration in intervals
. 225
5.2.1
Main assertions
. 225
5.2.2
Comments and inequalities
. 228
5.3
Multivariate integration
. 231
5.3.1
Integration in squares
. 231
5.3.2
Integration in cubes
. 236
5.3.3
Integration based on logarithmic spaces
. 240
5.4
Integration in planar domains
. 243
5.4.1
Introduction, definitions
. 243
5.4.2
Spaces with dominating mixed smoothness, integration
. 245
6
Discrepancy
248
6.1
Introduction, definitions
. 248
6.1.1
Definitions
. 248
6.1.2
The one-dimensional case
. 251
6.2
Relationships between integral and
discrepane}'
numbers
. 252
6.2.1
Prerequisites
.,,,.,.,, 252
6.2.2
Hlawka-Zaremba identity
.,.,,.,.,,,,., 255
6.2.3
Equivalences
.,.,,.,.,.,.,, 257
6.3
Discrepancy numbers
. 258
6.3.1
Main assertions
.,.,.,.,,,,,,,,,. 258
6.3.2
The one-dimensional case, revisited
.,.,.,. 262
6.3.3
Comments, problems, proposals
.,.,,.,,,,,. 269
Bibliography
275
List of Figures
289
Symbols
291
Index
295 |
| any_adam_object | 1 |
| author | Triebel, Hans 1936- |
| author_GND | (DE-588)133515923 |
| author_facet | Triebel, Hans 1936- |
| author_role | aut |
| author_sort | Triebel, Hans 1936- |
| author_variant | h t ht |
| building | Verbundindex |
| bvnumber | BV037277851 |
| classification_rvk | SK 280 |
| classification_tum | MAT 655f MAT 410f MAT 464f |
| ctrlnum | (OCoLC)699795248 (DE-599)BVBBV037277851 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037277851 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-26T10:00:35Z |
| institution | BVB |
| isbn | 9783037190852 |
| language | English |
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| physical | IX, 296 Seiten Diagramme |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | European Mathematical Society |
| record_format | marc |
| series | EMS tracts in mathematics |
| series2 | EMS tracts in mathematics |
| spelling | Triebel, Hans 1936- Verfasser (DE-588)133515923 aut Bases in function spaces, sampling, discrepancy, numerical integration Hans Triebel Zürich European Mathematical Society [2010] © 2010 IX, 296 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier EMS tracts in mathematics 11 Basis Mathematik (DE-588)4228195-7 gnd rswk-swf Numerische Integration (DE-588)4172168-8 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Funktionenraum (DE-588)4134834-5 s Basis Mathematik (DE-588)4228195-7 s Numerische Integration (DE-588)4172168-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-03719-585-7 (DE-604)BV036739628 EMS tracts in mathematics 11 (DE-604)BV022480257 11 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021190682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Triebel, Hans 1936- Bases in function spaces, sampling, discrepancy, numerical integration EMS tracts in mathematics Basis Mathematik (DE-588)4228195-7 gnd Numerische Integration (DE-588)4172168-8 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4228195-7 (DE-588)4172168-8 (DE-588)4134834-5 |
| title | Bases in function spaces, sampling, discrepancy, numerical integration |
| title_auth | Bases in function spaces, sampling, discrepancy, numerical integration |
| title_exact_search | Bases in function spaces, sampling, discrepancy, numerical integration |
| title_full | Bases in function spaces, sampling, discrepancy, numerical integration Hans Triebel |
| title_fullStr | Bases in function spaces, sampling, discrepancy, numerical integration Hans Triebel |
| title_full_unstemmed | Bases in function spaces, sampling, discrepancy, numerical integration Hans Triebel |
| title_short | Bases in function spaces, sampling, discrepancy, numerical integration |
| title_sort | bases in function spaces sampling discrepancy numerical integration |
| topic | Basis Mathematik (DE-588)4228195-7 gnd Numerische Integration (DE-588)4172168-8 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Basis Mathematik Numerische Integration Funktionenraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021190682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022480257 |
| work_keys_str_mv | AT triebelhans basesinfunctionspacessamplingdiscrepancynumericalintegration |