Theory of function spaces: 3
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2006
|
| Schriftenreihe: | Monographs in mathematics
100 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 426 S. |
| ISBN: | 3764375817 9783764375812 |
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| 245 | 1 | 0 | |a Theory of function spaces |n 3 |c Hans Triebel |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2006 | |
| 300 | |a XII, 426 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs in mathematics |v 100 | |
| 490 | 0 | |a Monographs in mathematics |v ... | |
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Datensatz im Suchindex
| _version_ | 1804141432130240512 |
|---|---|
| adam_text | Contents
List of Figures
..................................
x
Preface
......................................
xj
1
How to Measure Smoothness
1.1
Introduction
............................... 1
1.2
Concrete spaces
............................. 2
1.3
The Fourier-analytical approach
.................... 4
1.4
Local means
............................... 9
1.5
Atoms
.................................. 12
1.5.1
Smooth atoms
......................... 12
1.5.2
Non-smooth atoms
....................... 15
1.5.3
A technical modification
.................... 18
1.6
Quarks
.................................. 19
1.7
Wavelet bases
.............................. 26
1.7.1
Multiresolution analysis
.................... 26
1.7.2 Haar
wavelets
.......................... 28
1.7.3
Smooth wavelets
........................ 30
1.8
Wavelet frames
............................. 35
1.9
Envelopes
................................ 39
1.9.1
Sharp embeddings
....................... 40
1.9.2
The critical case
........................ 45
1.9.3
The super-critical case
..................... 48
1.9.4
The sub-critical case
...................... 51
1.9.5
Some generalisations and further references
......... 52
1.10
Compactness in quasi-Banach spaces
................. 55
1.11
Function spaces on domains
...................... 58
1.11.1
General domains: definitions, embeddings
.......... 58
1.11.2
General domains: entropy numbers
.............. 60
1.11.3
General domains: atoms
.................... 61
1.11.4
Lipschitz domains: definitions
................. 63
1.11.5
Lipschitz domains: extension
................. 64
1.11.6
Lipschitz domains: subspaces
................. 66
vi
Contents
1.11.7
Lipschitz
domains: approximation
numbers
......... 67
1.11.8
Lipschitz domains: interpolation
............... 69
1.11.9
Characterisations by differences
................ 72
1.11.
lOLipschitz domains: Sobolev,
Ilölder-Zygmund
spaces
.... 76
1.11.11
General domains: sharp embeddings and envelopes
..... 77
1.12
Fractal measures
............................ 78
1.12.1
An introduction to the non-smooth
.............. 78
1.12.2
Radon measures
........................ 80
1.12.3
The /.¿-property
......................... 81
1.13
Fractal operators
............................ 85
1.13.1
The classical theory
...................... 85
1.13.2
The fractal theory
....................... 87
1.14
Fractal characteristics of measures
.................. 92
1.15 Isotropie
measures
........................... 95
1.15.1
Some notation and basic assertions
.............. 95
1.15.2
Traces and fractal operators
.................. 97
1.16
Weyl measures
............................. 99
1.17
Spaces on fractals and on quasi-metric spaces
............ 101
1.17.1
Fractal characteristics, revisited
................ 101
1.17.2
Traces and trace spaces
.................... 103
1.17.3
Quarkonial representations
.................. 109
1.17.4
Quasi-metric spaces
...................... 112
1.17.5
Spaces on quasi-metric spaces
................. 115
1.17.6
Function spaces on d-spaces
.................. 119
1.18
Fractal characteristics of distributions
................ 121
1.19
A black sheep becomes the king
.................... 122
2
Atoms and Pointwise Multipliers
2.1
Notation, definitions and basic assertions
.............. 127
2.1.1
An introductory remark
.................... 127
2.1.2
Basic notation
......................... 127
2.1.3
Spaces on Euclidean n-space
................. 128
2.1.4
Smooth atoms
......................... 130
2.2
Non-smooth atomic decompositions
.................. 131
2.3
Pointwise multipliers and self-similar spaces
............. 136
2.3.1
Definitions and preliminaries
................. 136
2.3.2
Uniform and self-similar spaces
................ 137
2.3.3
Pointwise multipliers
...................... 140
2.3.4
Comments and complements
................. 144
Contents
vii
3
Wavelets
3.1
Wavelet isomorphisms and wavelet bases
............... 147
3.1.1
Definitions
........................... 147
3.1.2
Some preparations
....................... 149
3.1.3
The main assertion
....................... 153
3.1.4
Two applications
........................ 157
3.1.5
Further wavelet isomorphisms
................. 159
3.2
Wavelet frames
............................. 161
3.2.1
Preliminaries and definitions
................. 161
3.2.2
Subatomic decompositions
................... 164
3.2.3
Wavelet frames for distributions
............... 170
3.2.4
Wavelet frames for functions
................. 174
3.2.5
Local smoothness theory
.................... 180
3.3
Complements
.............................. 186
3.3.1
Gausslets
............................ 186
3.3.2
Positivity
............................ 190
4
Spaces on Domains, Wavelets, Sampling Numbers
4.1
Spaces on Lipschitz domains
...................... 193
4.1.1
introduction
.......................... 193
4.1.2
Definitions
........................... 194
4.1.3
Further spaces, some embeddings
............... 195
4.1.4
Intrinsic characterisations
................... 198
4.2
Wavelet para-bases
........................... 203
4.2.1
Wavelets in Euclidean n-space, revisited
........... 203
4.2.2
Scaling properties
....................... 205
4.2.3
Refined localisation
....................... 207
4.2.4
Wavelets in domains: positive smoothness
.......... 209
4.2.5
Wavelets in domains: general smoothness
.......... 214
4.3
Sampling numbers
........................... 218
4.3.1
Definitions
........................... 218
4.3.2
Basic properties
........................ 220
4.3.3
Main assertions
......................... 222
4.4
Complements
.............................. 228
4.4.1
Relations to other numbers
.................. 228
4.4.2
Embedding constants
..................... 231
5 Anisotropie
Function Spaces
5.1
Definitions and basic properties
.................... 235
5.1.1
Introduction
.......................... 235
5.1.2
Definitions
........................... 237
5.1.3
Concrete spaces
......................... 239
5.1.4
New developments
....................... 243
5.1.5
Atoms
.............................. 244
5.1.6
Local means
........................... 247
Contents
5.1.7
A comment on dual pairings
................. 248
5.2
Wavelets
................................. 249
5.2.1 Anisotropie multiresolution
analysis
............. 249
5.2.2
Main assertions
......................... 252
5.3
The transference method
........................ 256
5.3.1
The method
........................... 256
5.3.2
Embeddings
........................... 258
5.3.3
Entropy numbers
........................ 258
5.3.4
Besov
characteristics
...................... 260
Weighted Function Spaces
6.1
Definitions and basic properties
.................... 263
6.1.1
Introduction
.......................... 263
6.1.2
Definitions
........................... 263
6.1.3
Basic properties
........................ 265
6.1.4
Special cases
.......................... 267
6.2
Wavelets
................................. 268
6.3
A digression: Sequence spaces
..................... 273
6.3.1
Basic, spaces
........................... 273
6.3.2
Modifications
.......................... 276
6.4
Entropy numbers
............................ 279
6.4.1
The mam case
......................... 279
6.4.2
The limiting case
......................... 284
6.5
Complements
.............................. 286
6.5.1
The transference method
................... 286
6.5.2
Radial spaces
.......................... 287
Fractal Analysis
7.1
Measures
................................ 297
7.1.1
Definitions, basic properties
.................. 297
7.1.2
Potentials and Fourier transforms
............... 300
7.1.3
Traces: general measures
.................... 303
7.1.4
Traces:
isotropie
measures
................... 307
7.2
Characteristics
............................. 313
7.2.1
Characteristics of measures
.................. 313
7.2.2
A digression: Adapted local means
.............. 319
7.2.3
Characteristics of distributions
................ 322
7.3
Operators
................................ 332
7.3.1
Potentials and the regularity of measures
.......... 332
7.3.2
Elliptic operators: general measures
............. 339
7.3.3
Elliptic operators:
isotropie
measures
............. 342
7.3.4
Weyl measures
......................... 344
Contents ix
8
Function
Spaces
on Quasi-metric Spaces
8.1
Spaces on d-sets
............................ 345
8.1.1
Introduction
.......................... 345
8.1.2
Quarkonial characterisations
................. 346
8.1.3
Atomic characterisations
.................... 350
8.2
Quasi-metric spaces
.......................... 357
8.2.1
d-spaces
............................. 357
8.2.2
Snowflaked transforms
..................... 359
8.3
Spaces on d-spaces
........................... 363
8.3.1
Frames
............................. 363
8.3.2
Spaces of positive smoothness
................. 365
8.3.3
Spaces of arbitrary smoothness
................ 367
8.3.4
Spaces of restricted smoothness
................ 368
8.4
Applications
............................... 371
8.4.1
Entropy numbers
........................ 371
8.4.2
Riesz potentials
......................... 372
8.4.3 Anisotropie
spaces
....................... 374
9
Function Spaces on Sets
9.1
Introduction and reproducing formula
................ 377
9.1.1
Introduction
.......................... 377
9.1.2
Reproducing formula
...................... 377
9.2
Spaces on Euclidean 71-space
...................... 381
9.2.1
Definitions and basic assertions
................ 381
9.2.2
Properties
............................
38G
9.3
Spaces on sets
.............................. 390
9.3.1
Preliminaries and sequence spaces
.............. 390
9.3.2
Function spaces
......................... 394
References
.................................... 397
Notational Agreements
............................. 417
Symbols
...................................... 419
Index
....................................... 423
|
| any_adam_object | 1 |
| author | Triebel, Hans 1936- |
| author_GND | (DE-588)133515923 |
| author_facet | Triebel, Hans 1936- |
| author_role | aut |
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| bvnumber | BV025971314 |
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| id | DE-604.BV025971314 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:15:46Z |
| institution | BVB |
| isbn | 3764375817 9783764375812 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019214661 |
| oclc_num | 181504352 |
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| owner | DE-11 DE-824 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-188 DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-11 DE-824 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-188 DE-83 DE-19 DE-BY-UBM |
| physical | XII, 426 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Triebel, Hans 1936- Verfasser (DE-588)133515923 aut Theory of function spaces 3 Hans Triebel Basel [u.a.] Birkhäuser 2006 XII, 426 S. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 100 Monographs in mathematics ... Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Funktionsraum (DE-588)4155697-5 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Funktionsraum (DE-588)4155697-5 s DE-604 Harmonische Analyse (DE-588)4023453-8 s Funktionenraum (DE-588)4134834-5 s (DE-604)BV004830065 3 Monographs in mathematics 100 (DE-604)BV000008284 100 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019214661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Triebel, Hans 1936- Theory of function spaces Monographs in mathematics Harmonische Analyse (DE-588)4023453-8 gnd Funktionsraum (DE-588)4155697-5 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4155697-5 (DE-588)4134834-5 |
| title | Theory of function spaces |
| title_auth | Theory of function spaces |
| title_exact_search | Theory of function spaces |
| title_full | Theory of function spaces 3 Hans Triebel |
| title_fullStr | Theory of function spaces 3 Hans Triebel |
| title_full_unstemmed | Theory of function spaces 3 Hans Triebel |
| title_short | Theory of function spaces |
| title_sort | theory of function spaces |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Funktionsraum (DE-588)4155697-5 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Harmonische Analyse Funktionsraum Funktionenraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019214661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004830065 (DE-604)BV000008284 |
| work_keys_str_mv | AT triebelhans theoryoffunctionspaces3 |