Metrics on the phase space and non-selfadjoint pseudo-differential operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2010
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| Schriftenreihe: | Pseudo-differential operators
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XI, 397 S. graph. Darst. |
| ISBN: | 9783764385095 |
Internformat
MARC
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| 245 | 1 | 0 | |a Metrics on the phase space and non-selfadjoint pseudo-differential operators |c Nicolas Lerner |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2010 | |
| 300 | |a XI, 397 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Literaturangaben | ||
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| 650 | 0 | 7 | |a Pseudodifferentialoperator |0 (DE-588)4047640-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtselbstadjungierter Operator |0 (DE-588)4405912-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Phasenraum |0 (DE-588)4139912-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-7643-8510-1 |
| 830 | 0 | |a Pseudo-differential operators |v 3 |w (DE-604)BV035815877 |9 3 | |
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Datensatz im Suchindex
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| adam_text | 2.2.5 ADMISSIBLE METRIC AND WEIGHTS 76 CONTENTS PREFACE IX 1 BASIC
NOTIONS OF PHASE SPACE ANALYSIS I 1.1 INTRODUCTION TO
PSEUDO-DIFFERENTIAL OPERATORS 1 1.1.1 PROLEGOMENA 1 1.1.2 QUANTIZATION
FORMULAS 9 1.1.3 THE 5]^ 0 CLASS OF SYMBOLS 11 1.1.4 THE SEMI-CLASSICAL
CALCULUS 22 1.1.5 OTHER CLASSES OF SYMBOLS 27 1.2 PSEUDO-DIFFERENTIAL
OPERATORS ON AN OPEN SUBSET OF K 28 1.2.1 INTRODUCTION 28 1.2.2
INVERSION OF (MICRO)ELLIPTIC OPERATORS 32 1.2.3 PROPAGATION OF
SINGULARITIES 37 1.2.4 LOCAL SOLVABILITY 42 1.3 PSEUDO-DIFFERENTIAL
OPERATORS IN HARMONIC ANALYSIS 51 1.3.1 SINGULAR INTEGRALS, EXAMPLES 51
1.3.2 REMARKS ON THE CALDERON-ZYGMUND THEORY AND CLASSICAL
PSEUDO-DIFFERENTIAL OPERATORS 54 2 METRICS ON THE PHASE SPACE 57 2.1 THE
STRUCTURE OF THE PHASE SPACE 57 2.1.1 SYMPLECTIC ALGEBRA 57 2.1.2 THE
WIGNER FUNCTION 58 2.1.3 QUANTIZATION FORMULAS 58 2.1.4 THE METAPLECTIC
GROUP 60 2.1.5 COMPOSITION FORMULA 62 2.2 ADMISSIBLE METRICS 67 2.2.1 A
SHORT REVIEW OF EXAMPLES OF PSEUDO-DIFFERENTIAL CALCULI . . 67 2.2.2
SLOWLY VARYING METRICS ON R 2N 68 2.2.3 THE UNCERTAINTY PRINCIPLE FOR
METRICS 72 2.2.4 TEMPERATE METRICS 74 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/995948372 DIGITALISIERT DURCH 2.2.6 THE MAIN DISTANCE
FUNCTION 80 2.3 GENERAL PRINCIPLES OF PSEUDO-DIFFERENTIAL CALCULUS 83
2.3.1 CONFINEMENT ESTIMATES 84 2.3.2 BICONFINEMENT ESTIMATES 84 2.3.3
SYMBOLIC CALCULUS 91 2.3.4 ADDITIONAL REMARKS 94 2.3.5 CHANGING THE
QUANTIZATION 100 2.4 THE WICK CALCULUS OF PSEUDO-DIFFERENTIAL OPERATORS
100 2.4.1 WICK QUANTIZATION 100 2.4.2 FOCK-BARGMANN SPACES 104 2.4.3 ON
THE COMPOSITION FORMULA FOR THE WICK QUANTIZATION ... 106 2.5 BASIC
ESTIMATES FOR PSEUDO-DIFFERENTIAL OPERATORS 110 2.5.1 I? ESTIMATES 110
2.5.2 THE GARDING INEQUALITY WITH GAIN OF ONE DERIVATIVE 113 2.5.3 THE
FEFFERMAN-PHONG INEQUALITY 115 2.5.4 ANALYTIC FUNCTIONAL CALCULUS 134
2.6 SOBOLEV SPACES ATTACHED TO A PSEUDO-DIFFERENTIAL CALCULUS 137 2.6.1
INTRODUCTION 137 2.6.2 DEFINITION OF THE SOBOLEV SPACES 138 2.6.3
CHARACTERIZATION OF PSEUDO-DIFFERENTIAL OPERATORS 140 2.6.4
ONE-PARAMETER GROUP OF ELLIPTIC OPERATORS 146 2.6.5 AN ADDITIONAL
HYPOTHESIS FOR THE WIENER LEMMA: THE GEODESIC TEMPERANCE 152 ESTIMATES
FOR NON-SELFADJOINT OPERATORS 161 3.1 INTRODUCTION 161 3.1.1 EXAMPLES
161 3.1.2 FIRST-BRACKET ANALYSIS 171 3.1.3 HEURISTICS ON CONDITION (ST)
174 3.2 THE GEOMETRY OF CONDITION (*) 177 3.2.1 DEFINITIONS AND EXAMPLES
177 3.2.2 CONDITION (P) 179 3.2.3 CONDITION ( &) FOR SEMI-CLASSICAL
FAMILIES OF FUNCTIONS .... 181 3.2. 3.5.2 THE TWO-DIMENSIONAL CASE, THE
OBLIQUE DERIVATIVE PROBLEM . 216 3.5.3 TRANSVERSAL SIGN CHANGES 220
3.5.4 SEMI-GLOBAL SOLVABILITY UNDER CONDITION (P) 225 3.6 (TY) DOES NOT
IMPLY SOLVABILITY WITH LOSS OF ONE DERIVATIVE 226 3.6.1 INTRODUCTION 226
3.6.2 CONSTRUCTION OF A COUNTEREXAMPLE 232 3.6.3 MORE ON THE STRUCTURE
OF THE COUNTEREXAMPLE 246 3.7 CONDITION (*) DOES IMPLY SOLVABILITY WITH
LOSS OF 3/2 DERIVATIVES . 250 3.7.1 INTRODUCTION 250 3.7.2 ENERGY
ESTIMATES 251 3.7.3 FROM SEMI-CLASSICAL TO LOCAL ESTIMATES 263 3.8
CONCLUDING REMARKS 283 3.8.1 A SHORT HISTORICAL ACCOUNT OF SOLVABILITY
QUESTIONS 283 3.8.2 OPEN PROBLEMS 284 3.8.3 PSEUDO-SPECTRUM AND
SOLVABILITY 285 APPENDIX 287 4.1 SOME ELEMENTS OF FOURIER ANALYSIS 287
4.1.1 BASICS 287 4.1.2 THE LOGARITHM OF A NON-SINGULAR SYMMETRIC MATRIX
289 4.1.3 FOURIER TRANSFORM OF GAUSSIAN FUNCTIONS 291 4.1.4 SOME
STANDARD EXAMPLES OF FOURIER TRANSFORM 295 4.1.5 THE HARDY OPERATOR 299
4.2 SOME REMARKS ON ALGEBRA 300 4.2.1 ON SIMULTANEOUS DIAGONALIZATION OF
QUADRATIC FORMS .... 300 4.2.2 SOME REMARKS ON COMMUTATIVE ALGEBRA 301
4.3 LEMMAS OF CLASSICAL ANALYSIS 303 4.3.1 ON THE FAAE DI BRUNO FORMULA
303 4.3.2 ON LEIBNIZ FORMULAS 305 4.3.3 ON SOBOLEV NORMS 306 4.3.4 ON
PARTITIONS OF UNITY 308 4.3.5 ON NON-NEGATIVE FUNCTIONS 310 4.3. 4.7 A
FEW ELEMENTS OF OPERATOR THEORY 356 4.7.1 A SELFADJOINT OPERATOR 356
4.7.2 COTLAR S LEMMA 357 4.7.3 SEMI-CLASSICAL FOURIER INTEGRAL OPERATORS
361 4.8 ON THE SJOESTRAND ALGEBRA 366 4.9 MORE ON SYMBOLIC CALCULUS 367
4.9.1 PROPERTIES OF SOME METRICS 367 4.9.2 PROOF OF LEMMA 3.2.12 ON THE
PROPER CLASS 368 4.9.3 MORE ELEMENTS OF WICK CALCULUS 370 4.9.4 SOME
LEMMAS ON SYMBOLIC CALCULUS 374 4.9.5 THE BEALS-FEFFERMAN REDUCTION 376
4.9.6 ON TENSOR PRODUCTS OF HOMOGENEOUS FUNCTIONS 378 4.9.7 ON THE
COMPOSITION OF SOME SYMBOLS 379 BIBLIOGRAPHY 383 INDEX 395
|
| any_adam_object | 1 |
| author | Lerner, Nicolas 1953- |
| author_GND | (DE-588)140393692 |
| author_facet | Lerner, Nicolas 1953- |
| author_role | aut |
| author_sort | Lerner, Nicolas 1953- |
| author_variant | n l nl |
| building | Verbundindex |
| bvnumber | BV025600157 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)506435480 (DE-599)BVBBV025600157 |
| dewey-full | 515.7242 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7242 |
| dewey-search | 515.7242 |
| dewey-sort | 3515.7242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV025600157 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:37:16Z |
| institution | BVB |
| isbn | 9783764385095 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020195689 |
| oclc_num | 506435480 |
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| owner_facet | DE-11 DE-19 DE-BY-UBM DE-824 |
| physical | XI, 397 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Pseudo-differential operators |
| series2 | Pseudo-differential operators |
| spelling | Lerner, Nicolas 1953- Verfasser (DE-588)140393692 aut Metrics on the phase space and non-selfadjoint pseudo-differential operators Nicolas Lerner Basel [u.a.] Birkhäuser 2010 XI, 397 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pseudo-differential operators 3 Literaturangaben Phasenraum (DE-588)4139912-2 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 s Nichtselbstadjungierter Operator (DE-588)4405912-7 s Phasenraum (DE-588)4139912-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-7643-8510-1 Pseudo-differential operators 3 (DE-604)BV035815877 3 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195689&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lerner, Nicolas 1953- Metrics on the phase space and non-selfadjoint pseudo-differential operators Pseudo-differential operators Phasenraum (DE-588)4139912-2 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd |
| subject_GND | (DE-588)4139912-2 (DE-588)4047640-6 (DE-588)4405912-7 |
| title | Metrics on the phase space and non-selfadjoint pseudo-differential operators |
| title_auth | Metrics on the phase space and non-selfadjoint pseudo-differential operators |
| title_exact_search | Metrics on the phase space and non-selfadjoint pseudo-differential operators |
| title_full | Metrics on the phase space and non-selfadjoint pseudo-differential operators Nicolas Lerner |
| title_fullStr | Metrics on the phase space and non-selfadjoint pseudo-differential operators Nicolas Lerner |
| title_full_unstemmed | Metrics on the phase space and non-selfadjoint pseudo-differential operators Nicolas Lerner |
| title_short | Metrics on the phase space and non-selfadjoint pseudo-differential operators |
| title_sort | metrics on the phase space and non selfadjoint pseudo differential operators |
| topic | Phasenraum (DE-588)4139912-2 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd |
| topic_facet | Phasenraum Pseudodifferentialoperator Nichtselbstadjungierter Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195689&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035815877 |
| work_keys_str_mv | AT lernernicolas metricsonthephasespaceandnonselfadjointpseudodifferentialoperators |