The analysis of linear partial differential operators: 1 Distribution theory and Fourier analysis
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1990
|
| Edition: | 2. ed |
| Series: | Grundlehren der mathematischen Wissenschaften
... |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus: |
| Physical Description: | XI, 440 S |
| ISBN: | 3540523456 0387523456 9783540006626 9783642614972 |
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| 245 | 1 | 0 | |a The analysis of linear partial differential operators |n 1 |p Distribution theory and Fourier analysis |c Lars Hörmander |
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Record in the Search Index
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| adam_text | LARS HOERMANDER THE ANALYSIS OF LINEAR PARTIAL DIFFERENTIAL OPERATORS I
DISTRIBUTION THEORY AND FOURIER ANALYSIS SECOND EDITION SPRINGER-VERLAG
BERLIN HEIDELBERG NEW YORK LONDON PARIS TOKYO HONGKONG CONTENTS
INTRODUCTION 1 CHAPTER I. TEST FUNCTIONS 5 SUMMARY 5 1.1. A REVIEW OF
DIFFERENTIAL CALCULUS 5 1.2. EXISTENCE OF TEST FUNCTIONS 14 1.3.
CONVOLUTION 16 1.4. CUTOFF FUNCTIONS AND PARTITIONS OF UNITY 25 NOTES 31
CHAPTER II. DEFINITION AND BASIC PROPERTIES OF DISTRIBUTIONS . . 33
SUMMARY 33 2.1. BASIC DEFINITIONS 33 2.2. LOCALIZATION 41 2.3.
DISTRIBUTIONS WITH COMPACT SUPPORT 44 NOTES 52 CHAPTER III.
DIFFERENTIATION AND MULTIPLICATION BY FUNCTIONS . . 54 SUMMARY 54 3.1.
DEFINITION AND EXAMPLES 54 3.2. HOMOGENEOUS DISTRIBUTIONS 68 3.3. SOME
FUNDAMENTAL SOLUTIONS 79 3.4. EVALUATION OF SOME INTEGRALS 84 NOTES 86
CHAPTER IV. CONVOLUTION 87 SUMMARY 87 4.1. CONVOLUTION WITH A SMOOTH
FUNCTION 88 4.2. CONVOLUTION OF DISTRIBUTIONS 100 4.3. THE THEOREM OF
SUPPORTS 105 4.4. THE ROLE OF FUNDAMENTAL SOLUTIONS 109 X CONTENTS 4.5.
BASIC II ESTIMATES FOR CONVOLUTIONS 116 NOTES 124 CHAPTER V.
DISTRIBUTIONS IN PRODUCT SPACES 126 SUMMARY 126 5.1. TENSOR PRODUCTS 126
5.2. THE KERNEL THEOREM 128 NOTES 132 CHAPTER VI. COMPOSITION WITH
SMOOTH MAPS 133 SUMMARY 133 6.1. DEFINITIONS 133 6.2. SOME FUNDAMENTAL
SOLUTIONS 137 6.3. DISTRIBUTIONS ON A MANIFOLD 142 6.4. THE TANGENT AND
COTANGENT BUNDLES 146 NOTES 156 CHAPTER VII. THE FOURIER TRANSFORMATION
158 SUMMARY 158 7.1. THE FOURIER TRANSFORMATION IN F AND IN SF 159
7.2. POISSON S SUMMATION FORMULA AND PERIODIC DISTRIBUTIONS 177 7.3. THE
FOURIER-LAPLACE TRANSFORMATION IN $ 181 7.4. MORE GENERAL
FOURIER-LAPLACE TRANSFORMS 191 7.5. THE MALGRANGE PREPARATION THEOREM
195 7.6. FOURIER TRANSFORMS OF GAUSSIAN FUNCTIONS 205 7.7. THE METHOD OF
STATIONARY PHASE 215 7.8. OSCILLATORY INTEGRALS 236 7.9. H (S) , * AND
HOLDER ESTIMATES 240 NOTES 248 CHAPTER VIII. SPECTRAL ANALYSIS OF
SINGULARITIES 251 SUMMARY 251 8.1. THE WAVE FRONT SET 252 8.2. A REVIEW
OF OPERATIONS WITH DISTRIBUTIONS 261 8.3. THE WAVE FRONT SET OF
SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS 271 8.4. THE WAVE FRONT SET
WITH RESPECT TO C L 280 8.5. RULES OF COMPUTATION FOR WF L 296 8.6. WF L
FOR SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS . . . 305 8.7.
MICROHYPERBOLICITY 317 NOTES 322 CONTENTS XI CHAPTER IX. HYPERFUNCTIONS
325 SUMMARY 325 9.1. ANALYTIC FUNCTIONAL 326 9.2. GENERAL HYPERFUNCTIONS
335 9.3. THE ANALYTIC WAVE FRONT SET OF A HYPERFUNCTION . . . . 338 9.4.
THE ANALYTIC CAUCHY PROBLEM 346 9.5. HYPERFUNCTION SOLUTIONS OF PARTIAL
DIFFERENTIAL EQUATIONS 353 9.6. THE ANALYTIC WAVE FRONT SET AND THE
SUPPORT 358 NOTES 368 EXERCISES 371 ANSWERS AND HINTS TO ALL THE
EXERCISES 394 BIBLIOGRAPHY 419 INDEX 437 INDEX OF NOTATION 439
|
| adam_txt |
LARS HOERMANDER THE ANALYSIS OF LINEAR PARTIAL DIFFERENTIAL OPERATORS I
DISTRIBUTION THEORY AND FOURIER ANALYSIS SECOND EDITION SPRINGER-VERLAG
BERLIN HEIDELBERG NEW YORK LONDON PARIS TOKYO HONGKONG CONTENTS
INTRODUCTION 1 CHAPTER I. TEST FUNCTIONS 5 SUMMARY 5 1.1. A REVIEW OF
DIFFERENTIAL CALCULUS 5 1.2. EXISTENCE OF TEST FUNCTIONS 14 1.3.
CONVOLUTION 16 1.4. CUTOFF FUNCTIONS AND PARTITIONS OF UNITY 25 NOTES 31
CHAPTER II. DEFINITION AND BASIC PROPERTIES OF DISTRIBUTIONS . . 33
SUMMARY 33 2.1. BASIC DEFINITIONS 33 2.2. LOCALIZATION 41 2.3.
DISTRIBUTIONS WITH COMPACT SUPPORT 44 NOTES 52 CHAPTER III.
DIFFERENTIATION AND MULTIPLICATION BY FUNCTIONS . . 54 SUMMARY 54 3.1.
DEFINITION AND EXAMPLES 54 3.2. HOMOGENEOUS DISTRIBUTIONS 68 3.3. SOME
FUNDAMENTAL SOLUTIONS 79 3.4. EVALUATION OF SOME INTEGRALS 84 NOTES 86
CHAPTER IV. CONVOLUTION 87 SUMMARY 87 4.1. CONVOLUTION WITH A SMOOTH
FUNCTION 88 4.2. CONVOLUTION OF DISTRIBUTIONS 100 4.3. THE THEOREM OF
SUPPORTS 105 4.4. THE ROLE OF FUNDAMENTAL SOLUTIONS 109 X CONTENTS 4.5.
BASIC II ESTIMATES FOR CONVOLUTIONS 116 NOTES 124 CHAPTER V.
DISTRIBUTIONS IN PRODUCT SPACES 126 SUMMARY 126 5.1. TENSOR PRODUCTS 126
5.2. THE KERNEL THEOREM 128 NOTES 132 CHAPTER VI. COMPOSITION WITH
SMOOTH MAPS 133 SUMMARY 133 6.1. DEFINITIONS 133 6.2. SOME FUNDAMENTAL
SOLUTIONS 137 6.3. DISTRIBUTIONS ON A MANIFOLD 142 6.4. THE TANGENT AND
COTANGENT BUNDLES 146 NOTES 156 CHAPTER VII. THE FOURIER TRANSFORMATION
158 SUMMARY 158 7.1. THE FOURIER TRANSFORMATION IN F AND IN SF" 159
7.2. POISSON'S SUMMATION FORMULA AND PERIODIC DISTRIBUTIONS 177 7.3. THE
FOURIER-LAPLACE TRANSFORMATION IN $' 181 7.4. MORE GENERAL
FOURIER-LAPLACE TRANSFORMS 191 7.5. THE MALGRANGE PREPARATION THEOREM
195 7.6. FOURIER TRANSFORMS OF GAUSSIAN FUNCTIONS 205 7.7. THE METHOD OF
STATIONARY PHASE 215 7.8. OSCILLATORY INTEGRALS 236 7.9. H (S) , * AND
HOLDER ESTIMATES 240 NOTES 248 CHAPTER VIII. SPECTRAL ANALYSIS OF
SINGULARITIES 251 SUMMARY 251 8.1. THE WAVE FRONT SET 252 8.2. A REVIEW
OF OPERATIONS WITH DISTRIBUTIONS 261 8.3. THE WAVE FRONT SET OF
SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS 271 8.4. THE WAVE FRONT SET
WITH RESPECT TO C L 280 8.5. RULES OF COMPUTATION FOR WF L 296 8.6. WF L
FOR SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS . . . 305 8.7.
MICROHYPERBOLICITY 317 NOTES 322 CONTENTS XI CHAPTER IX. HYPERFUNCTIONS
325 SUMMARY 325 9.1. ANALYTIC FUNCTIONAL 326 9.2. GENERAL HYPERFUNCTIONS
335 9.3. THE ANALYTIC WAVE FRONT SET OF A HYPERFUNCTION . . . . 338 9.4.
THE ANALYTIC CAUCHY PROBLEM 346 9.5. HYPERFUNCTION SOLUTIONS OF PARTIAL
DIFFERENTIAL EQUATIONS 353 9.6. THE ANALYTIC WAVE FRONT SET AND THE
SUPPORT 358 NOTES 368 EXERCISES 371 ANSWERS AND HINTS TO ALL THE
EXERCISES 394 BIBLIOGRAPHY 419 INDEX 437 INDEX OF NOTATION 439 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:13:10Z |
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| institution | BVB |
| isbn | 3540523456 0387523456 9783540006626 9783642614972 |
| language | English |
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| physical | XI, 440 S |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
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| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Hörmander, Lars 1931-2012 Verfasser (DE-588)105823449 aut The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander 2. ed Berlin [u.a.] Springer 1990 XI, 440 S txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften ... Aus: Linearer partieller Differentialoperator (DE-588)4167722-5 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 s DE-604 Linearer partieller Differentialoperator (DE-588)4167722-5 s (DE-604)BV021850563 1 Erscheint auch als Online-Ausgabe 978-3-642-61497-2 Grundlehren der mathematischen Wissenschaften ... (DE-604)BV000000395 256 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015261247&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hörmander, Lars 1931-2012 The analysis of linear partial differential operators Grundlehren der mathematischen Wissenschaften Linearer partieller Differentialoperator (DE-588)4167722-5 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd |
| subject_GND | (DE-588)4167722-5 (DE-588)4167708-0 |
| title | The analysis of linear partial differential operators |
| title_auth | The analysis of linear partial differential operators |
| title_exact_search | The analysis of linear partial differential operators |
| title_exact_search_txtP | The analysis of linear partial differential operators |
| title_full | The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander |
| title_fullStr | The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander |
| title_full_unstemmed | The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander |
| title_short | The analysis of linear partial differential operators |
| title_sort | the analysis of linear partial differential operators distribution theory and fourier analysis |
| topic | Linearer partieller Differentialoperator (DE-588)4167722-5 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd |
| topic_facet | Linearer partieller Differentialoperator Lineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015261247&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021850563 (DE-604)BV000000395 |
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