Pseudodifferential and singular integral operators: an introduction with applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2012
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| Series: | De Gruyter graduate lectures
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 222 S. graph. Darst. |
| ISBN: | 9783110250305 |
Staff View
MARC
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| 100 | 1 | |a Abels, Helmut |d 1975- |e Verfasser |0 (DE-588)136678769 |4 aut | |
| 245 | 1 | 0 | |a Pseudodifferential and singular integral operators |b an introduction with applications |c Helmut Abels |
| 264 | 1 | |a Berlin [u.a.] |b De Gruyter |c 2012 | |
| 300 | |a X, 222 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter graduate lectures | |
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Record in the Search Index
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IMAGE 1
CONTENTS
PREFACE V
1 INTRODUCTION 1
1 FOURIER TRANSFORMATION AND PSEUDODIFFERENTIAL OPERATORS
2 FOURIER TRANSFORMATION AND TEMPERED DISTRIBUTIONS 9
2.1 DEFINITION AND BASIC PROPERTIES 9
2.2 RAPIDLY DECREASING FUNCTIONS - S(R") 13
2.3 INVERSE FOURIER TRANSFORMATION AND PLANCHEREL'S THEOREM 15
2.4 TEMPERED DISTRIBUTIONS AND FOURIER TRANSFORMATION 20
2.5 FOURIER TRANSFORMATION AND CONVOLUTION OF TEMPERED DISTRIBUTIONS .
23
2.6 CONVOLUTION ON S'(M. N ) AND FUNDAMENTAL SOLUTIONS 25
2.7 SOBOLEV AND BESSEL POTENTIAL SPACES 27
2.8 VECTOR-VALUED FOURIER-TRANSFORMATION 30
2.9 FINAL REMARKS AND EXERCISES 33
2.9.1 FURTHER READING 33
2.9.2 EXERCISES 34
3 BASIC CALCULUS OF PSEUDODIFFERENTIAL OPERATORS ON W 40
3.1 SYMBOL CLASSES AND BASIC PROPERTIES 40
3.2 COMPOSITION OF PSEUDODIFFERENTIAL OPERATORS: MOTIVATION 45
3.3 OSCILLATORY INTEGRALS 46
3.4 DOUBLE SYMBOLS 51
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1018440712
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
3.5 COMPOSITION OF PSEUDODIFFERENTIAL OPERATORS 54
3.6 APPLICATION: ELLIPTIC PSEUDODIFFERENTIAL OPERATORS AND PARAMETRICES
. 57
3.7 BOUNDEDNESS ON C(R") AND UNIQUENESS OF THE SYMBOL 63
3.8 ADJOINTS OF PSEUDODIFFERENTIAL OPERATORS AND OPERATORS IN
(JC, Y)-FORM 65
3.9 BOUNDEDNESS ON L 2 (M") AND L 2 -BESSEL POTENTIAL SPACES 68
3.10 OUTLOOK: COORDINATE TRANSFORMATIONS AND PSDOS ON MANIFOLDS . . .
74
3.11 FINAL REMARKS AND EXERCISES 77
3.11.1 FURTHER READING 77
3.11.2 EXERCISES 78
II SINGULAR INTEGRAL OPERATORS
4 TRANSLATION INVARIANT SINGULAR INTEGRAL OPERATORS 85
4.1 MOTIVATION 85
4.2 MAIN RESULT IN THE TRANSLATION INVARIANT CASE 87
4.3 CALDERON-ZYGMUND DECOMPOSITION AND THE MAXIMAL OPERATOR . . . 91
4.4 PROOF OF THE MAIN RESULT IN THE TRANSLATION INVARIANT CASE 95
4.5 EXAMPLES OF SINGULAR INTEGRAL OPERATORS 100
4.6 MIKHLIN MULTIPLIER THEOREM 107
4.7 OUTLOOK: HARDY SPACES AND BMO 112
4.8 FINAL REMARKS AND EXERCISES 118
4.8.1 FURTHER READING 118
4.8.2 EXERCISES 118
5 NON-TRANSLATION INVARIANT SINGULAR INTEGRAL OPERATORS 122
5.1 MOTIVATION 122
5.2 EXTENSION TO NON-TRANSLATION INVARIANT AND VECTOR-VALUED SINGULAR
INTEGRAL OPERATORS 124
5.3 HILBERT-SPACE-VALUED MIKHLIN MULTIPLIER THEOREM 129
IMAGE 3
CONTENTS IX
5.4 KERNEL REPRESENTATION OF A PSEUDODIFFERENTIAL OPERATOR 133
5.5 CONSEQUENCES OF THE KERNEL REPRESENTATION 140
5.6 FINAL REMARKS AND EXERCISES 143
5.6.1 FURTHER READING 143
5.6.2 EXERCISES 144
III APPLICATIONS TO FUNCTION SPACE AND DIFFERENTIAL EQUATIONS
6 INTRODUCTION TO BESOV AND BESSEL POTENTIAL SPACES 149
6.1 MOTIVATION 149
6.2 A FOURIER-ANALYTIC CHARACTERIZATION OF HOLDER CONTINUITY 150
6.3 BESSEL POTENTIAL AND BESOV SPACES - DEFINITIONS AND BASIC PROPERTIES
153
6.4 SOBOLEV EMBEDDINGS 160
6.5 EQUIVALENT NORMS 162
6.6 PSEUDODIFFERENTIAL OPERATORS ON BESOV SPACES 164
6.7 FINAL REMARKS AND EXERCISES 168
6.7.1 FURTHER READING 168
6.7.2 EXERCISES 168
7 APPLICATIONS TO ELLIPTIC AND PARABOLIC EQUATIONS 171
7.1 APPLICATIONS OF THE MIKHLIN MULTIPLIER THEOREM 171
7.1.1 RESOLVENT OF THE LAPLACE OPERATOR 171
7.1.2 SPECTRUM OF MULTIPLIER OPERATORS WITH HOMOGENEOUS SYMBOLS 174
7.1.3 SPECTRUM OF A CONSTANT COEFFICIENT DIFFERENTIAL OPERATOR . . 177
7.2 APPLICATIONS OF THE HILBERT-SPACE-VALUED MIKHLIN MULTIPLIER THEOREM
180 7.2.1 MAXIMAL REGULARITY OF ABSTRACT ODES IN HILBERT SPACES 180
7.2.2 HILBERT-SPACE VALUED BESSEL POTENTIAL AND SOBOLEV SPACES . 185
7.3 APPLICATIONS OF PSEUDODIFFERENTIAL OPERATORS 186
7.3.1 ELLIPTIC REGULARITY FOR ELLIPTIC PSEUDODIFFERENTIAL OPERATORS .
186
7.3.2 RESOLVENTS OF PARAMETER-ELLIPTIC DIFFERENTIAL OPERATORS 188 7.3.3
APPLICATION OF RESOLVENT ESTIMATES TO PARABOLIC INITIAL VALUE PROBLEMS
193
IMAGE 4
CONTENTS
7.4 FINAL REMARKS AND EXERCISES 194
7.4.1 FURTHER READING 194
7.4.2 EXERCISES 195
IV APPENDIX
A BASIC RESULTS FROM ANALYSIS 199
A.1 NOTATION AND FUNCTIONS ON M" 199
A.2 LEBESGUE INTEGRAL AND L P -SPACES 201
A.3 LINEAR OPERATORS AND DUAL SPACES 206
A.4 BOCHNER INTEGRAL AND VECTOR-VALUED L^-SPACES 209
A.5 FRECHET SPACES 212
A.6 EXERCISES 216
BIBLIOGRAPHY 217
INDEX 221 |
| any_adam_object | 1 |
| author | Abels, Helmut 1975- |
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| bvnumber | BV039557727 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)751007521 (DE-599)GBV665756763 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-15T00:07:00Z |
| institution | BVB |
| isbn | 9783110250305 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024409474 |
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| physical | X, 222 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate lectures |
| spelling | Abels, Helmut 1975- Verfasser (DE-588)136678769 aut Pseudodifferential and singular integral operators an introduction with applications Helmut Abels Berlin [u.a.] De Gruyter 2012 X, 222 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate lectures Singulärer Integraloperator (DE-588)4131249-1 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 s Singulärer Integraloperator (DE-588)4131249-1 s DE-604 Erscheint auch als Online-Ausgabe 978-3-11-025031-2 (DE-604)BV042348143 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409474&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abels, Helmut 1975- Pseudodifferential and singular integral operators an introduction with applications Singulärer Integraloperator (DE-588)4131249-1 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| subject_GND | (DE-588)4131249-1 (DE-588)4047640-6 |
| title | Pseudodifferential and singular integral operators an introduction with applications |
| title_auth | Pseudodifferential and singular integral operators an introduction with applications |
| title_exact_search | Pseudodifferential and singular integral operators an introduction with applications |
| title_full | Pseudodifferential and singular integral operators an introduction with applications Helmut Abels |
| title_fullStr | Pseudodifferential and singular integral operators an introduction with applications Helmut Abels |
| title_full_unstemmed | Pseudodifferential and singular integral operators an introduction with applications Helmut Abels |
| title_short | Pseudodifferential and singular integral operators |
| title_sort | pseudodifferential and singular integral operators an introduction with applications |
| title_sub | an introduction with applications |
| topic | Singulärer Integraloperator (DE-588)4131249-1 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| topic_facet | Singulärer Integraloperator Pseudodifferentialoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409474&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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