Hypo-analytic structures: local theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
1992
|
| Schriftenreihe: | Princeton mathematical series
40 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 497 S. |
| ISBN: | 069108744X |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804122053461147648 |
|---|---|
| adam_text | Contents
Preface xiii
I
Formally and Locally Integrable Structures.
Basic Definitions 3
1.1 Involutive systems of linear PDE defined by complex vector
fields. Formally and locally integrable structures 5
1.2 The characteristic set. Partial classification of formally
integrable structures 11
1.3 Strongly noncharacteristic, totally real, and maximally real
submanifolds 16
1.4 Noncharacteristic and totally characteristic submanifolds 23
1.5 Local representations 27
1.6 The associated differential complex 32
1.7 Local representations in locally integrable structures 39
1.8 The Levi form in a formally integrable structure 46
1.9 The Levi form in a locally integrable structure 49
1.10 Characteristics in real and in analytic structures 56
1.11 Orbits and leaves. Involutive structures of finite type 63
1.12 A model case: Tube structures 68
Notes 71
II
Local Approximation and Representation
in Locally Integrable Structures 73
II. 1 The coarse local embedding 76
n.2 The approximation formula 81
II. 3 Consequences and generalizations 86
II.4 Analytic vectors 94
viii Contents
II.5 Local structure of distribution solutions and of L closed
currents 100
II. 6 The approximate Poincard lemma 104
II.7 Approximation and local structure of solutions based on the fine
local embedding 108
II. 8 Unique continuation of solutions 115
Notes 119
III
Hypo Analytic Structures.
Hypocomplex Manifolds 120
HI. 1 Hypo analytic structures 121
III.2 Properties of hypo analytic functions 128
HI.3 Submanifolds compatible with the hypo analytic structure 130
111.4 Unique continuation of solutions in a hypo analytic manifold 137
111.5 Hypocomplex manifolds. Basic properties 145
111.6 Two dimensional hypocomplex manifolds 152
Appendix to Section III.6: Some lemmas about first order
differential operators 159
111.7 A class of hypocomplex CR manifolds 162
Notes 166
IV
Integrable Formal Structures.
Normal Forms 167
IV. 1 Integrable formal structures 168
IV.2 Hormander numbers, multiplicities, weights. Normal forms 174
IV.3 Lemmas about weights and vector fields 178
IV.4 Existence of basic vector fields of weight 1 185
IV.5 Existence of normal forms. Pluriharmonic free normal forms.
Rigid structures 191
IV.6 Leading parts 198
Notes 200
Contents tx
V
Involutive Structures
with Boundary 201
V. 1 Involutive structures with boundary 202
V.2 The associated differential complex. The boundary complex 209
V.3 Locally integrable structures with boundary. The Mayer
Vietoris sequence 219
V.4 Approximation of classical solutions in locally integrable
structures with boundary 226
V.5 Distribution solutions in a manifold with totally characteristic
boundary 228
V.6 Distribution solutions in a manifold with noncharacteristic
boundary 235
V.7 Example: Domains in complex space 246
Notes 251
VI
Local Integrability
and Local Solvability
in Elliptic Structures 252
VI. 1 The Bochner Martinelli formulas 253
VI.2 Homotopy formulas for 5 in convex and bounded domains 258
VI.3 Estimating the sup norms of the homotopy operators 264
VI.4 Holder estimates for the homotopy operators in concentric
balls 269
VI.5 The Newlander Nirenberg theorem 281
VI.6 End of the proof of the Newlander Nirenberg theorem 287
VI.7 Local integrability and local solvability of elliptic structures.
Levi flat structures 291
VI.8 Partial local group structures 297
VI.9 Involutive structures with transverse group action.
Rigid structures. Tube structures 303
Notes 310
x Contents
VII
Examples of Nonintegrability and
ofNonsolvability 312
VII. 1 Mizohata structures 314
VII.2 Nonsolvability and nonintegrability when the signature of
the Levi form is n 2| 319
VII. 3 Mizohata structures on two dimensional manifolds 324
VII.4 Nonintegrability and nonsolvability when the cotangent
structure bundle has rank one 330
VII.5 Nonintegrability and nonsolvability in Lewy structures.
The three dimensional case 337
VII.6 Nonintegrability in Lewy structures. The higher dimensional
case 343
VII.7 Example of a CR structure that is not locally integrable but
is locally integrable on one side 348
Notes 350
vin
Necessary Conditions for the Vanishing
of the Cohomology. Local Solvability
of a Single Vector Field 352
VIII. 1 Preliminary necessary conditions for exactness 354
VIII.2 Exactness of top degree forms 358
VIII. 3 A necessary condition for local exactness based on the
Levi form 364
VIH.4 A result about structures whose characteristic set has rank
at most equal to one 367
Vin.5 Proof of Theorem VHI.4.1 373
VHI.6 Applications of Theorem Vffl.4.1 378
Appendix to Section VIII.6: The current £„,„ 388
VIII.7 The case of a single vector field: Property (9 ) 389
VIII. 8 Sufficiency of Condition (9 ): Existence of L2 solutions 394
Appendix to Section VIII. 8: A Whitney lemma 402
VIII.9 Application of the Approximate Poincare lemma to the
existence of smooth solutions 404
Contents xi
VIII. 10 Necessity of Condition (9s) 407
Appendix to Section VIII. 10: Lemmas about real vector fields 411
Notes 413
IX
FBI Transform in a Hypo Analytic Manifold 415
IX. 1 FBI transform in a maximally real submanifold of complex
space 418
IX.2 The real structure bundle of a maximally real submanifold.
Well positioned maximally real submanifolds of Cm.
Inverting the FBI transform of a compactly supported
distribution 420
IX. 3 Holomorphic extendability of a distribution characterized
by the rate of decay of its FBI transform 426
IX.4 Smoothness of a distribution characterized by the rate of
decay of its FBI transform 428
IX.5 FBI transform in a hypo analytic manifold 433
IX.6 The FBI minitransform 438
IX.7 Propagation of hypo analyticity 442
Notes 449
X
Involutive Systems of Nonlinear
First Order Differential Equations 451
X. 1 Involutive systems of first order nonlinear PDE 453
X.2 Local representations 460
X.3 Microlocal integrability. First results on uniqueness in
the Cauchy problem 464
X.4 Quasilinear systems of differential equations with vector
valued unknown 469
X.5 The approximation formula 474
X.6 Uniqueness in the Cauchy problem 479
X.7 Approximation by smooth solutions 481
Notes 483
References 485
Index 493
|
| any_adam_object | 1 |
| author | Trèves, François 1930- |
| author_GND | (DE-588)107758652 |
| author_facet | Trèves, François 1930- |
| author_role | aut |
| author_sort | Trèves, François 1930- |
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| building | Verbundindex |
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| classification_rvk | SK 540 |
| classification_tum | MAT 582f MAT 332f MAT 474f |
| ctrlnum | (OCoLC)246626637 (DE-599)BVBBV007693050 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007693050 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:07:46Z |
| institution | BVB |
| isbn | 069108744X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005049704 |
| oclc_num | 246626637 |
| open_access_boolean | |
| owner | DE-739 DE-355 DE-BY-UBR DE-12 DE-91G DE-BY-TUM DE-29T DE-19 DE-BY-UBM DE-11 DE-188 |
| owner_facet | DE-739 DE-355 DE-BY-UBR DE-12 DE-91G DE-BY-TUM DE-29T DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | XVII, 497 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Princeton mathematical series |
| series2 | Princeton mathematical series |
| spelling | Trèves, François 1930- Verfasser (DE-588)107758652 aut Hypo-analytic structures local theory François Treves Princeton, NJ Princeton Univ. Press 1992 XVII, 497 S. txt rdacontent n rdamedia nc rdacarrier Princeton mathematical series 40 Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Vektorfeld (DE-588)4139571-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Überbestimmtes System (DE-588)4236167-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Vektorfeld (DE-588)4139571-2 s Komplexe Mannigfaltigkeit (DE-588)4031996-9 s DE-604 Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Lineare partielle Differentialgleichung (DE-588)4167708-0 s Überbestimmtes System (DE-588)4236167-9 s 2\p DE-604 Princeton mathematical series 40 (DE-604)BV000019035 40 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005049704&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Trèves, François 1930- Hypo-analytic structures local theory Princeton mathematical series Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Vektorfeld (DE-588)4139571-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Überbestimmtes System (DE-588)4236167-9 gnd |
| subject_GND | (DE-588)4167708-0 (DE-588)4031996-9 (DE-588)4139571-2 (DE-588)4037379-4 (DE-588)4044779-0 (DE-588)4236167-9 |
| title | Hypo-analytic structures local theory |
| title_auth | Hypo-analytic structures local theory |
| title_exact_search | Hypo-analytic structures local theory |
| title_full | Hypo-analytic structures local theory François Treves |
| title_fullStr | Hypo-analytic structures local theory François Treves |
| title_full_unstemmed | Hypo-analytic structures local theory François Treves |
| title_short | Hypo-analytic structures |
| title_sort | hypo analytic structures local theory |
| title_sub | local theory |
| topic | Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Vektorfeld (DE-588)4139571-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Überbestimmtes System (DE-588)4236167-9 gnd |
| topic_facet | Lineare partielle Differentialgleichung Komplexe Mannigfaltigkeit Vektorfeld Mannigfaltigkeit Partielle Differentialgleichung Überbestimmtes System |
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