Fourier integrals in classical analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1993
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
105 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 236 S. graph. Darst. |
| ISBN: | 0521434645 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface page ix
0. Background 1
0.1. Fourier Transform 1
0.2. Basic Real Variable Theory 9
0.3. Fractional Integration and Sobolev Embedding
Theorems 22
0.4. Wave Front Sets and the Cotangent Bundle 28
0.5. Oscillatory Integrals 36
Notes 39
1. Stationary Phase 40
1.1. Stationary Phase Estimates 40
1.2. Fourier Transform of Surface carried Measures 49
Notes 54
2. Non homogeneous Oscillatory Integral Operators 55
2.1. Non degenerate Oscillatory Integral Operators 56
2.2. Oscillatory Integral Operators Related to the
Restriction Theorem 58
2.3. Riesz Means in Rn 65
2.4. Kakeya Maximal Functions and Maximal Riesz
Means in R2 71
Notes 92
3. Pseudo differential Operators 93
3.1. Some Basics 93
3.2. Equivalence of Phase Functions 100
3.3. Self adjoint Elliptic Pseudo differential Operators on
Compact Manifolds 106
Notes 112
4. The Half wave Operator and Functions of
Pseudo differential Operators 113
4.1. The Half wave Operator 114
4.2. The Sharp Weyl Formula 124
4.3. Smooth Functions of Pseudo differential Operators 131
Notes 133
viii Contents
5. Lp Estimates of Eigenfunctions 135
5.1. The Discrete L2 Restriction Theorem 136
5.2. Estimates for Riesz Means 149
5.3. More General Multiplier Theorems 153
Notes 158
6. Fourier Integral Operators 160
6.1. Lagrangian Distributions 161
6.2. Regularity Properties 168
6.3. Spherical Maximal Theorems: Take 1 186
Notes 193
7. Local Smoothing of Fourier Integral Operators 194
7.1. Local Smoothing in Two Dimensions and Variable
Coefficient Kakeya Maximal Theorems 195
7.2. Local Smoothing in Higher Dimensions 214
7.3. Spherical Maximal Theorems Revisited 224
Notes 227
Appendix: Lagrangian Subspaces of T*TRn 228
Bibliography 230
Index 237
Index of Notation 238
|
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| indexdate | 2024-07-09T17:08:54Z |
| institution | BVB |
| isbn | 0521434645 |
| language | English |
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| physical | X, 236 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
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| spelling | Sogge, Christopher D. 1960- Verfasser (DE-588)104999275X aut Fourier integrals in classical analysis Christopher D. Sogge 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1993 X, 236 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 105 Eigenwertverteilung - Fourier-Integraloperator Partielle Differentialgleichung - Pseudodifferentialoperator - Fourier-Integral - Mikrolokale Analysis Analysis (DE-588)4001865-9 gnd rswk-swf Fourier-Integraloperator (DE-588)4155104-7 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Fourier-Integral (DE-588)4121290-3 gnd rswk-swf Fourier-Integral (DE-588)4121290-3 s DE-604 Fourier-Integraloperator (DE-588)4155104-7 s Harmonische Analyse (DE-588)4023453-8 s Analysis (DE-588)4001865-9 s DE-188 Cambridge tracts in mathematics 105 (DE-604)BV000000001 105 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005096759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sogge, Christopher D. 1960- Fourier integrals in classical analysis Cambridge tracts in mathematics Eigenwertverteilung - Fourier-Integraloperator Partielle Differentialgleichung - Pseudodifferentialoperator - Fourier-Integral - Mikrolokale Analysis Analysis (DE-588)4001865-9 gnd Fourier-Integraloperator (DE-588)4155104-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Integral (DE-588)4121290-3 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4155104-7 (DE-588)4023453-8 (DE-588)4121290-3 |
| title | Fourier integrals in classical analysis |
| title_auth | Fourier integrals in classical analysis |
| title_exact_search | Fourier integrals in classical analysis |
| title_full | Fourier integrals in classical analysis Christopher D. Sogge |
| title_fullStr | Fourier integrals in classical analysis Christopher D. Sogge |
| title_full_unstemmed | Fourier integrals in classical analysis Christopher D. Sogge |
| title_short | Fourier integrals in classical analysis |
| title_sort | fourier integrals in classical analysis |
| topic | Eigenwertverteilung - Fourier-Integraloperator Partielle Differentialgleichung - Pseudodifferentialoperator - Fourier-Integral - Mikrolokale Analysis Analysis (DE-588)4001865-9 gnd Fourier-Integraloperator (DE-588)4155104-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Integral (DE-588)4121290-3 gnd |
| topic_facet | Eigenwertverteilung - Fourier-Integraloperator Partielle Differentialgleichung - Pseudodifferentialoperator - Fourier-Integral - Mikrolokale Analysis Analysis Fourier-Integraloperator Harmonische Analyse Fourier-Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005096759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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