Function spaces, entropy numbers, differential operators:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
120 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 252 S. graph. Darst. |
| ISBN: | 0521560365 |
Staff View
MARC
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| 245 | 1 | 0 | |a Function spaces, entropy numbers, differential operators |c D. E. Edmunds ; H. Triebel |
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Record in the Search Index
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| adam_text | Contents
Preface page ix
1 The Abstract Background 1
1.1 Introduction 1
1.2 Spectral theory in quasi Banach spaces 1
1.3 Entropy numbers and approximation numbers 7
1.3.1 Definitions and elementary properties 7
1.3.2 Interpolation properties of entropy numbers 13
1.3.3 Relationships between entropy and approximation numbers 15
1.3.4 Connections with eigenvalues 18
2 Function Spaces 23
2.1 Introduction 23
2.2 The spaces Bspq and Fspq on R 24
2.2.1 Definitions 24
2.2.2 Concrete spaces 25
2.2.3 Atomic representations 28
2.3 Special properties 32
2.3.1 Dilations 32
2.3.2 Localisation 35
2.3.3 Embeddings 43
2.4 Holder inequalities 45
2.4.1 Preliminaries 45
2.4.2 Paramultiplication 47
2.4.3 The main theorem 51
2.4.4 Limiting cases 55
2.4.5 Holder inequalities for Hp 56
2.5 The spaces Bpq and Fspq on domains 57
2.5.1 Definitions 57
v
vi Contents
2.5.2 Atoms and atomic domains 60
2.5.3 Atomic representations 63
2.6 The spaces Lp(log L)a and logarithmic Sobolev spaces 65
2.6.1 Definitions and preliminaries 65
2.6.2 Basic theorems 69
2.6.3 Logarithmic Sobolev spaces 75
2.7 Limiting embeddings 81
2.7.1 Extremal functions 81
2.7.2 Embedding constants 89
2.7.3 Embeddings 92
3 Entropy and Approximation Numbers of Embeddings 96
3.1 Introduction 96
3.2 The embedding ofY™ in ^ 97
3.2.1 The spaces *7 97
3.2.2 Entropy numbers 98
3.2.3 Approximation numbers 101
3.3 Embeddings between function spaces 105
3.3.1 Notation 105
3.3.2 Entropy numbers: upper estimates 105
3.3.3 Entropy numbers: lower estimates 114
3.3.4 Approximation numbers 119
3.3.5 Historical remarks 126
3.4 Limiting embeddings in spaces of Orlicz type 128
3.4.1 Preliminaries 128
3.4.2 Embeddings in L«,(log L)_fl(fl) 129
3.4.3 Interior estimates 138
3.4.4 Duality arguments 150
3.5 Embeddings in non smooth domains 151
4 Weighted Function Spaces and Entropy Numbers 153
4.1 Introduction 153
4.2 Weighted spaces 153
4.2.1 Definitions 153
4.2.2 Basic properties 156
4.2.3 Embeddings: general weights 160
4.2.4 Embeddings: the weights (x)* 162
4.2.5 Holder inequalities 164
4.3 Entropy numbers 165
4.3.1 A preparation 165
4.3.2 The main theorem 168
Contents vii
4.3.3 Approximation numbers 179
5 Elliptic Operators 184
5.1 Introduction 184
5.2 Elliptic operators in domains: non limiting cases 185
5.2.1 Introduction; the Birman Schwinger principle 185
5.2.2 Elliptic differential operators: mapping properties 187
5.2.3 Pseudodifferential operators: mapping properties 189
5.2.4 Elliptic operators: spectral properties 192
5.2.5 Elliptic operators: generalisations 199
5.2.6 Pseudodifferential operators: spectral properties 205
5.2.7 The negative spectrum 206
5.3 Elliptic operators in domains: limiting cases 207
5.3.1 Introduction 207
5.3.2 Orlicz spaces 207
5.3.3 Logarithmic Sobolev spaces 213
5.4 Elliptic operators in R 221
5.4.1 Introduction; the Birman Schwinger principle revisited 221
5.4.2 Pseudodifferential operators: mapping properties 224
5.4.3 Pseudodifferential operators: spectral properties 227
5.4.4 Degenerate pseudodifferential operators: eigenvalue distri¬
butions 228
5.4.5 Degenerate pseudodifferential operators: smoothness theory 232
5.4.6 Degenerate pseudodifferential operators of positive order 234
5.4.7 The negative spectrum: basic results 236
5.4.8 The negative spectrum: splitting techniques 238
5.4.9 The negative spectrum: homogeneity arguments 240
References 243
Index of Symbols 249
Index 251
|
| any_adam_object | 1 |
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| dewey-full | 515.73 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.73 |
| dewey-search | 515.73 |
| dewey-sort | 3515.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| institution | BVB |
| isbn | 0521560365 |
| language | English |
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| physical | XI, 252 S. graph. Darst. |
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| spelling | Edmunds, David E. 1931- Verfasser (DE-588)129315176 aut Function spaces, entropy numbers, differential operators D. E. Edmunds ; H. Triebel 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1996 XI, 252 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 120 Eigenwert (DE-588)4151200-5 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Entropie (DE-588)4014894-4 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Funktionenraum (DE-588)4134834-5 s Entropie (DE-588)4014894-4 s Differentialoperator (DE-588)4012251-7 s DE-604 Eigenwert (DE-588)4151200-5 s Triebel, Hans 1936- Verfasser (DE-588)133515923 aut Cambridge tracts in mathematics 120 (DE-604)BV000000001 120 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007368275&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Edmunds, David E. 1931- Triebel, Hans 1936- Function spaces, entropy numbers, differential operators Cambridge tracts in mathematics Eigenwert (DE-588)4151200-5 gnd Differentialoperator (DE-588)4012251-7 gnd Entropie (DE-588)4014894-4 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4151200-5 (DE-588)4012251-7 (DE-588)4014894-4 (DE-588)4134834-5 |
| title | Function spaces, entropy numbers, differential operators |
| title_auth | Function spaces, entropy numbers, differential operators |
| title_exact_search | Function spaces, entropy numbers, differential operators |
| title_full | Function spaces, entropy numbers, differential operators D. E. Edmunds ; H. Triebel |
| title_fullStr | Function spaces, entropy numbers, differential operators D. E. Edmunds ; H. Triebel |
| title_full_unstemmed | Function spaces, entropy numbers, differential operators D. E. Edmunds ; H. Triebel |
| title_short | Function spaces, entropy numbers, differential operators |
| title_sort | function spaces entropy numbers differential operators |
| topic | Eigenwert (DE-588)4151200-5 gnd Differentialoperator (DE-588)4012251-7 gnd Entropie (DE-588)4014894-4 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Eigenwert Differentialoperator Entropie Funktionenraum |
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