The technique of pseudodifferential operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1995
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society: London Mathematical Society lecture note series
202 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 382 S. |
| ISBN: | 0521378648 |
Internformat
MARC
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| 100 | 1 | |a Cordes, Heinz O. |d 1925- |e Verfasser |0 (DE-588)1014418356 |4 aut | |
| 245 | 1 | 0 | |a The technique of pseudodifferential operators |c H. O. Cordes |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XII, 382 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society: London Mathematical Society lecture note series |v 202 | |
| 650 | 4 | |a Pseudodifferentialoperator | |
| 650 | 0 | 7 | |a Pseudodifferentialoperator |0 (DE-588)4047640-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Pseudodifferentialoperator |0 (DE-588)4047640-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a London Mathematical Society: London Mathematical Society lecture note series |v 202 |w (DE-604)BV000000130 |9 202 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006715036 | ||
Datensatz im Suchindex
| _version_ | 1804124505626378240 |
|---|---|
| adam_text | TABLE OF CONTENTS
Chapter 0. Introductory discussions 1
0.0. Some special notations, used in the book 1
0.1. The Fourier transform; elementary facts 3
0.2. Fourier analysis for temperate distributions on fcn 9
0.3. The Paley Wiener theorem; Fourier transform for
general u6 D 14
0.4. The Fourier Laplace method; examples 20
0.5. Abstract solutions and hypo ellipticity 30
0.6. Exponentiating a first order linear differential
operator 31
0.7. Solving a nonlinear first order partial differen¬
tial equation 36
0.8. Characteristics and bicharacteristics of a linear
PDE 40
0.9. Lie groups and Lie algebras for classical analysts 45
Chapter 1. Calculus of pseudodifferential operators 52
1.0. Introduction 52
1.1. Definition of i|)do s 52
1.2. Elementary properties of T|do s 56
1.3. Hoermander symbols; Weyl x| do s; distribution
kernels 60
1.4. The composition formulas of Beals 64
1.5. The Leibniz formulas with integral remainder 69
1.6. Calculus of i|Jdo s for symbols of Hoermander type 72
1.7. Strictly classical symbols; some lemmata for
application 78
Chapter 2. Elliptic operators and parametrices in ln 81
2.0. Introduction 81
2.1. Elliptic and md elliptic ipdo s 82
2.2. Formally hypo elliptic pdo s 84
2.3. Local md ellipticity and local md hypo ellipticity 87
2.4. Formally hypo elliptic differential expressions 91
2.5. The wave front set and its invariance under ipdo s 93
yjjj Contents
2.6. Systems of tjxio s 97
Chapter 3. L Sobolev theory and applications 99
3.0. Introduction 99
3.1. L2 boundedness of zero order ijdo s 99
3.2. L boundedness for the case of 6 0 103
3.3. Weighted Sobolev spaces; K parametrix and Green
inverse 106
3.4. Existence of a Green inverse 113
3.5. H compactness for tpdo s of negative order 117
Chapter 4. Pseudodifferential operators on manifolds with
conical ends 118
4.0. Introduction 118
4.1. Distributions and temperate distributions on
manifolds 119
4.2. Distributions on S manifolds; manifolds with
conical ends 123
4.3. Coordinate invariance of pseudodifferential
operators 129
4.4. Pseudodifferential operators on S manifolds 134
4.5. Order classes and Green inverses on S manifolds 139
Chapter 5. Elliptic and parabolic problems 144
5.0. Introduction 144
5.1. Elliptic problems in free space; a summary 147
5.2. The elliptic boundary problem 149
5.3. Conversion to an Kn problem of Riemann Hilbert
type 154
5.4. Boundary hypo ellipticity; asymptotic expansion
mod ay 157
5.5. A system of i|de s for the ij . of problem 3.4 162
5.6. Lopatinskij Shapiro conditions; normal solvabi¬
lity of (2.2) . 169
5.7. Hypo ellipticity, and the classical parabolic
problem 174
5.8. Spectral and semi group theory for ipdo s 179
5.9. Self adjointness for boundary problems 186
5.10. C algebras of xldo s; comparison algebras 189
Chapter 6. Hyperbolic first order systems 196
6.0. Introduction 196
6.1. First order symmetric hyperbolic systems of PDE 196
6.2. First order symmetric hyperbolic systems of
ijxle s on Kn . 200
6.3. The evolution operator and its properties 206
Contents ix
6.4. N th order strictly hyperbolic systems and
symmetrizers. 210
6.5. The particle flow of a single hyperbolic ijxie 215
6.6. The action of the particle flow on symbols 219
6.7. Propagation of maximal ideals and propagation
of singularities 223
Chapter 7. Hyperbolic differential equations 226
7.0. Introduction 226
7.1. Algebra of hyperbolic polynomials 227
7.2. Hyperbolic polynomials and characteristic surfaces 230
7.3. The hyperbolic Cauchy problem for variable
coefficients 235
7.4. The cone h for a strictly hyperbolic expression
of type e1 238
7.5. Regions of dependence and influence; finite
propagation speed 241
7.6. The local Cauchy problem; hyperbolic problems
on manifolds 244
Chapter 8. Pseudodifferential operators as smooth
operators of L(H) 247
8.0. Introduction 247
8.1. |xJo s as smooth operators of £(#,,) 248
8.2. The IDO theorem 251
8.3. The other half of the TOO theorem 257
8.4. Smooth operators; the i|) algebra property;
•vjxHo calculus 261
8.5. The operator classes *K?S and 1GL , and their
symbols 265
8.6 The Frechet algebras i[ x , and the Weinstein
Zelditch class 271
8.7 Polynomials in x and dx with coefficients in 1GX 275
8.8 Characterization of 1GX by the Lie algebra 279
Chapter 9. Particle flow and invariant algebra of a semi
strictly hyperbolic system; coordinate invariance
of Opijur^. 282
9.0. Introduction 282
9.1. Flow invariance of xp2 283
9.2. Invariance of ijis under particle flows 286
9.3. Conjugation of Optyx with e , KG Opi| ce 289
9.4. Coordinate and gauge invariance; extension to
S manifolds 293
1 TCt*
9.5. Conjugation with e for a matrix valued K=k(x,D) 296
x Contents
9.6. A technical discussion of commutator equations 301
9.7. Completion of the proof of theorem 5.4 305
Chapter 10. The invariant algebra of the Dirac equation 310
10.0. Introduction 310
10.1. A refinement of the concept of observable 314
10.2. The invariant algebra and the Foldy Wouthuysen
transform 319
10.3. The geometrical optics approach for the Dirac
algebra P 324
10.4. Some identities for the Dirac matrices 329
10.5. The first correction zQ for standard observables 334
10.6. Proof of the Foldy Wouthuysen theorem 343
10.7. Nonscalar symbols in diagonal coordinates of h(x,|) 350
10.8. The full symmetrized first correction symbol zg 356
10.9. Some final remarks 367
References 370
Index 380
|
| any_adam_object | 1 |
| author | Cordes, Heinz O. 1925- |
| author_GND | (DE-588)1014418356 |
| author_facet | Cordes, Heinz O. 1925- |
| author_role | aut |
| author_sort | Cordes, Heinz O. 1925- |
| author_variant | h o c ho hoc |
| building | Verbundindex |
| bvnumber | BV010112995 |
| classification_rvk | SI 320 SK 620 |
| ctrlnum | (OCoLC)246644630 (DE-599)BVBBV010112995 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010112995 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:46:44Z |
| institution | BVB |
| isbn | 0521378648 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006715036 |
| oclc_num | 246644630 |
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| owner_facet | DE-355 DE-BY-UBR DE-384 DE-12 DE-703 DE-634 DE-11 DE-188 |
| physical | XII, 382 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Cordes, Heinz O. 1925- Verfasser (DE-588)1014418356 aut The technique of pseudodifferential operators H. O. Cordes 1. publ. Cambridge u.a. Cambridge Univ. Press 1995 XII, 382 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 202 Pseudodifferentialoperator Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 s DE-604 London Mathematical Society: London Mathematical Society lecture note series 202 (DE-604)BV000000130 202 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006715036&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cordes, Heinz O. 1925- The technique of pseudodifferential operators London Mathematical Society: London Mathematical Society lecture note series Pseudodifferentialoperator Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| subject_GND | (DE-588)4047640-6 |
| title | The technique of pseudodifferential operators |
| title_auth | The technique of pseudodifferential operators |
| title_exact_search | The technique of pseudodifferential operators |
| title_full | The technique of pseudodifferential operators H. O. Cordes |
| title_fullStr | The technique of pseudodifferential operators H. O. Cordes |
| title_full_unstemmed | The technique of pseudodifferential operators H. O. Cordes |
| title_short | The technique of pseudodifferential operators |
| title_sort | the technique of pseudodifferential operators |
| topic | Pseudodifferentialoperator Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| topic_facet | Pseudodifferentialoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006715036&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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