The analysis of linear partial differential operators: 2 Differential operators with constant coefficients
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1990
|
| Edition: | 2. rev. print |
| Series: | Grundlehren der mathematischen Wissenschaften
... |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | VIII, 390 S |
| ISBN: | 3540121390 0387121390 3540225161 |
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| 245 | 1 | 0 | |a The analysis of linear partial differential operators |n 2 |p Differential operators with constant coefficients |c Lars Hörmander |
| 250 | |a 2. rev. print | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1990 | |
| 300 | |a VIII, 390 S | ||
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| adam_text | LARS HOERMANDER THE ANALYSIS OF LINEAR PARTIAL DIFFERENTIAL OPERATORS II
DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS SPRINGER-VERLAG BERLIN
HEIDELBERG NEW YORK LONDON PARIS TOKYO HONG KONG CONTENTS INTRODUCTION 1
CHAPTER X. EXISTENCE AND APPROXIMATION OF SOLUTIONS OF DIFFERENTIAL
EQUATIONS 3 SUMMARY 3 10.1. THE SPACES B PK 3 10.2. FUNDAMENTAL
SOLUTIONS 16 10.3. THE EQUATION P( ) M =/WHEN FEG 29 10.4. COMPARISON
OF DIFFERENTIAL OPERATORS 32 10.5. APPROXIMATION OF SOLUTIONS OF
HOMOGENEOUS DIFFERENTIAL EQUATIONS 39 10.6. THE EQUATION P{D) U =F WHEN
/ IS IN A LOCAL SPACE =9 F 41 10.7. THE EQUATION P(D)U=F WHEN FE@ {X)
45 10.8. THE GEOMETRICAL MEANING OF THE CONVEXITY CONDITIONS . 50 NOTES
58 CHAPTER XL INTERIOR REGULARITY OF SOLUTIONS OF DIFFERENTIAL EQUATIONS
60 SUMMARY 60 11.1. HYPOELLIPTIC OPERATORS . . N. 61 11.2. PARTIALLY
HYPOELLIPTIC OPERATORS 69 11.3. CONTINUATION OF DIFFERENTIABILITY 73
11.4. ESTIMATES FOR DERIVATIVES OF HIGH ORDER 85 NOTES 92 CHAPTER XII.
THE CAUCHY AND MIXED PROBLEMS 94 SUMMARY 94 12.1. THE CAUCHY PROBLEM FOR
THE WAVE EQUATION 96 12.2. THE OSCILLATORY CAUCHY PROBLEM FOR THE WAVE
EQUATION. 104 12.3. NECESSARY CONDITIONS FOR EXISTENCE AND UNIQUENESS OF
SOLUTIONS TO THE CAUCHY PROBLEM 110 CONTENTS VII 12.4. PROPERTIES OF
HYPERBOLIC POLYNOMIALS 112 12.5. THE CAUCHY PROBLEM FOR A HYPERBOLIC
EQUATION . . . .120 12.6. THE SINGULARITIES OF THE FUNDAMENTAL SOLUTION
125 12.7. A GLOBAL UNIQUENESS THEOREM 133 12.8. THE CHARACTERISTIC
CAUCHY PROBLEM 143 12.9. MIXED PROBLEMS 162 NOTES 180 CHAPTER XIII.
DIFFERENTIAL OPERATORS OF CONSTANT STRENGTH . . .182 SUMMARY 182 13.1.
DEFINITIONS AND BASIC PROPERTIES 182 13.2. EXISTENCE THEOREMS WHEN THE
COEFFICIENTS ARE MERELY CONTINUOUS 184 13.3. EXISTENCE THEOREMS WHEN THE
COEFFICIENTS ARE IN C . .186 13.4. HYPOELLIPTICITY 191 13.5. GLOBAL
EXISTENCE THEOREMS 194 13.6. NON-UNIQUENESS FOR THE CAUCHY PROBLEM 201
NOTES 224 CHAPTER XIV. SCATTERING THEORY 225 SUMMARY 225 14.1. SOME
FUNCTION SPACES 227 14.2. DIVISION BY FUNCTIONS WITH SIMPLE ZEROS 232
14.3. THE RESOLVENT OF THE UNPERTURBED OPERATOR 237 14.4. SHORT RANGE
PERTURBATIONS 243 14.5. THE BOUNDARY VALUES OF THE RESOLVENT AND THE
POINT SPECTRUM 251 14.6. THE DISTORTED FOURIER TRANSFORMS AND THE
CONTINUOUS SPECTRUM 255 14.7. ABSENCE OF EMBEDDED EIGENVALUES 264 NOTES
268 CHAPTER XV. ANALYTIC FUNCTION THEORY AND DIFFERENTIAL EQUATIONS 270
SUMMARY 270 15.1. THE INHOMOGENEOUS CAUCHY-RIEMANN EQUATIONS . . . .271
15.2. THE FOURIER-LAPLACE TRANSFORM OF B 2 K (X) WHEN X IS CONVEX 279
15.3. FOURIER-LAPLACE REPRESENTATION OF SOLUTIONS OF DIFFERENTIAL
EQUATIONS 287 VIII CONTENTS 15.4. THE FOURIER-LAPLACE TRANSFORM OF C*(X)
WHEN X IS CONVEX 296 NOTES 300 CHAPTER XVI. CONVOLUTION EQUATIONS 302
SUMMARY 302 16.1. SUBHARMONIC FUNCTIONS 303 16.2. PLURISUBHARMONIC
FUNCTIONS 314 16.3. THE SUPPORT AND SINGULAR SUPPORT OF A CONVOLUTION .
.319 16.4. THE APPROXIMATION THEOREM 335 16.5. THE INHOMOGENEOUS
CONVOLUTION EQUATION 341 16.6. HYPOELLIPTIC CONVOLUTION EQUATIONS 353
16.7. HYPERBOLIC CONVOLUTION EQUATIONS 356 NOTES 360 APPENDIX A. SOME
ALGEBRAIC LEMMAS 362 A.L. THE ZEROS OF ANALYTIC FUNCTIONS 362 A.2.
ASYMPTOTIC PROPERTIES OF ALGEBRAIC FUNCTIONS OF SEVERAL VARIABLES 364
NOTES 371 BIBLIOGRAPHY 373 INDEX 391 INDEX OF NOTATION 392
|
| adam_txt |
LARS HOERMANDER THE ANALYSIS OF LINEAR PARTIAL DIFFERENTIAL OPERATORS II
DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS SPRINGER-VERLAG BERLIN
HEIDELBERG NEW YORK LONDON PARIS TOKYO HONG KONG CONTENTS INTRODUCTION 1
CHAPTER X. EXISTENCE AND APPROXIMATION OF SOLUTIONS OF DIFFERENTIAL
EQUATIONS 3 SUMMARY 3 10.1. THE SPACES B PK 3 10.2. FUNDAMENTAL
SOLUTIONS 16 10.3. THE EQUATION P( ) M =/WHEN FEG' 29 10.4. COMPARISON
OF DIFFERENTIAL OPERATORS 32 10.5. APPROXIMATION OF SOLUTIONS OF
HOMOGENEOUS DIFFERENTIAL EQUATIONS 39 10.6. THE EQUATION P{D) U =F WHEN
/ IS IN A LOCAL SPACE =9' F 41 10.7. THE EQUATION P(D)U=F WHEN FE@'{X)
45 10.8. THE GEOMETRICAL MEANING OF THE CONVEXITY CONDITIONS . 50 NOTES
58 CHAPTER XL INTERIOR REGULARITY OF SOLUTIONS OF DIFFERENTIAL EQUATIONS
60 SUMMARY 60 11.1. HYPOELLIPTIC OPERATORS . . N. 61 11.2. PARTIALLY
HYPOELLIPTIC OPERATORS 69 11.3. CONTINUATION OF DIFFERENTIABILITY 73
11.4. ESTIMATES FOR DERIVATIVES OF HIGH ORDER 85 NOTES 92 CHAPTER XII.
THE CAUCHY AND MIXED PROBLEMS 94 SUMMARY 94 12.1. THE CAUCHY PROBLEM FOR
THE WAVE EQUATION 96 12.2. THE OSCILLATORY CAUCHY PROBLEM FOR THE WAVE
EQUATION. 104 12.3. NECESSARY CONDITIONS FOR EXISTENCE AND UNIQUENESS OF
SOLUTIONS TO THE CAUCHY PROBLEM 110 CONTENTS VII 12.4. PROPERTIES OF
HYPERBOLIC POLYNOMIALS 112 12.5. THE CAUCHY PROBLEM FOR A HYPERBOLIC
EQUATION . . . .120 12.6. THE SINGULARITIES OF THE FUNDAMENTAL SOLUTION
125 12.7. A GLOBAL UNIQUENESS THEOREM 133 12.8. THE CHARACTERISTIC
CAUCHY PROBLEM 143 12.9. MIXED PROBLEMS 162 NOTES 180 CHAPTER XIII.
DIFFERENTIAL OPERATORS OF CONSTANT STRENGTH . . .182 SUMMARY 182 13.1.
DEFINITIONS AND BASIC PROPERTIES 182 13.2. EXISTENCE THEOREMS WHEN THE
COEFFICIENTS ARE MERELY CONTINUOUS 184 13.3. EXISTENCE THEOREMS WHEN THE
COEFFICIENTS ARE IN C . .186 13.4. HYPOELLIPTICITY 191 13.5. GLOBAL
EXISTENCE THEOREMS 194 13.6. NON-UNIQUENESS FOR THE CAUCHY PROBLEM 201
NOTES 224 CHAPTER XIV. SCATTERING THEORY 225 SUMMARY 225 14.1. SOME
FUNCTION SPACES 227 14.2. DIVISION BY FUNCTIONS WITH SIMPLE ZEROS 232
14.3. THE RESOLVENT OF THE UNPERTURBED OPERATOR 237 14.4. SHORT RANGE
PERTURBATIONS 243 14.5. THE BOUNDARY VALUES OF THE RESOLVENT AND THE
POINT SPECTRUM 251 14.6. THE DISTORTED FOURIER TRANSFORMS AND THE
CONTINUOUS SPECTRUM 255 14.7. ABSENCE OF EMBEDDED EIGENVALUES 264 NOTES
268 CHAPTER XV. ANALYTIC FUNCTION THEORY AND DIFFERENTIAL EQUATIONS 270
SUMMARY 270 15.1. THE INHOMOGENEOUS CAUCHY-RIEMANN EQUATIONS . . . .271
15.2. THE FOURIER-LAPLACE TRANSFORM OF B 2 K (X) WHEN X IS CONVEX 279
15.3. FOURIER-LAPLACE REPRESENTATION OF SOLUTIONS OF DIFFERENTIAL
EQUATIONS 287 VIII CONTENTS 15.4. THE FOURIER-LAPLACE TRANSFORM OF C*(X)
WHEN X IS CONVEX 296 NOTES 300 CHAPTER XVI. CONVOLUTION EQUATIONS 302
SUMMARY 302 16.1. SUBHARMONIC FUNCTIONS 303 16.2. PLURISUBHARMONIC
FUNCTIONS 314 16.3. THE SUPPORT AND SINGULAR SUPPORT OF A CONVOLUTION .
.319 16.4. THE APPROXIMATION THEOREM 335 16.5. THE INHOMOGENEOUS
CONVOLUTION EQUATION 341 16.6. HYPOELLIPTIC CONVOLUTION EQUATIONS 353
16.7. HYPERBOLIC CONVOLUTION EQUATIONS 356 NOTES 360 APPENDIX A. SOME
ALGEBRAIC LEMMAS 362 A.L. THE ZEROS OF ANALYTIC FUNCTIONS 362 A.2.
ASYMPTOTIC PROPERTIES OF ALGEBRAIC FUNCTIONS OF SEVERAL VARIABLES 364
NOTES 371 BIBLIOGRAPHY 373 INDEX 391 INDEX OF NOTATION 392 |
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| institution | BVB |
| isbn | 3540121390 0387121390 3540225161 |
| language | English |
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| physical | VIII, 390 S |
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| 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 2 Differential operators with constant coefficients Lars Hörmander 2. rev. print Berlin [u.a.] Springer 1990 VIII, 390 S txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften ... Hier auch später erschienene, unveränderte Nachdrucke (DE-604)BV021850563 2 Grundlehren der mathematischen Wissenschaften ... (DE-604)BV000000395 257 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015261249&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 |
| 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 2 Differential operators with constant coefficients Lars Hörmander |
| title_fullStr | The analysis of linear partial differential operators 2 Differential operators with constant coefficients Lars Hörmander |
| title_full_unstemmed | The analysis of linear partial differential operators 2 Differential operators with constant coefficients Lars Hörmander |
| title_short | The analysis of linear partial differential operators |
| title_sort | the analysis of linear partial differential operators differential operators with constant coefficients |
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