Differential equations on complex manifolds:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1994
|
| Schriftenreihe: | Mathematics and its applications
276 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 504 S. graph. Darst. |
| ISBN: | 0792327101 |
Internformat
MARC
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| 100 | 1 | |a Sternin, Boris Ju. |d 1939- |e Verfasser |0 (DE-588)120484536 |4 aut | |
| 245 | 1 | 0 | |a Differential equations on complex manifolds |c by Boris Sternin and Victor Shatalov |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1994 | |
| 300 | |a XII, 504 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 276 | |
| 650 | 4 | |a Differential equations | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexe Mannigfaltigkeit |0 (DE-588)4031996-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | 1 | |a Komplexe Mannigfaltigkeit |0 (DE-588)4031996-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Šatalov, Viktor E. |d 1945- |e Verfasser |0 (DE-588)120484544 |4 aut | |
| 830 | 0 | |a Mathematics and its applications |v 276 |w (DE-604)BV008163334 |9 276 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006577352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006577352 | ||
Datensatz im Suchindex
| _version_ | 1804124294766133248 |
|---|---|
| adam_text | Contents
Preface xi
Introduction 1
0.1 Generalities 1
0.2 The Integral Transformation 4
0.3 Differential Equations with Constant Coefficients .... 14
0.4 Elementary Solutions 22
0.5 Continuation of Solutions to Elliptic Equations 30
0.5.1 Statement of the Problem 30
0.5.2 Complexification of the Continuation Problem . . 36
0.5.3 Examples 38
1 Some Questions of Analysis and Geometry of Complex
Manifolds 41
1.1 Summary of Results 41
1.1.1 Leray s Residues 42
1.1.2 Function Spaces 46
1.1.3 Parameter Dependent Integrals 49
1.1.4 Homogeneous Functions and Projective Spaces . . 53
1.2 Multidimensional Residue Theory 55
1.2.1 Motivations 55
1.2.2 Fibre Bundles and Induced Homomorphisms on
(Co)homology 59
1.2.3 The Bundle Structure on a Tubular Neighbour¬
hood of a Manifold 65
1.2.4 Definition of Residue 67
1.2.5 Leray s Residues 72
v
vi CONTENTS
1.3 Function Spaces 74
1.3.1 Motivations and Basic Definitions 75
1.3.2 Properties of the Function Spaces 77
1.4 Parameter Dependent Integrals 84
1.4.1 General Remarks 84
1.4.2 Examples 85
1.4.3 Thorn s Triviality Theorem (Isotopy Lemma) ... 91
1.4.4 Ramified Homology Classes 95
1.4.5 Differentiation Formula for Parameter Dependent
Integrals 101
1.5 Homogeneous Functions and Projective Spaces 104
1.5.1 General Remarks 104
1.5.2 Projective Spaces 105
1.5.3 Holomorphic Forms on Projective Spaces 107
1.6 Integration on Fibre Bundles 113
1.6.1 Motivations 113
1.6.2 Relative Spectral Sequence on Homology 124 r
1.6.3 Construction of the Boundary Homomorphism . . 127
1.6.4 Leray s Homomorphisms in E™ 128
1.6.5 Relative Spectral Sequence on Cohomology and
Duality 130
1.6.6 Definition of Repeated Integrals 132
2 Symplectic and Contact Structures 137
2.1 Main Definitions 137
2.1.1 Preliminary Remarks 137
2.1.2 Homogeneous Symplectic Structure and Contact
Structure 140
2.2 Symplectization and Contactization 143
2.2.1 Contactization of a Symplectic Structure 143
2.2.2 Symplectization of a Contact Structure 145
2.2.3 The Contact Product of Contact Structures ... 148
2.3 Symplectic and Contact Transformations 150
2.3.1 Contact and Symplectic Biholomorphisms .... 150
2.3.2 Hamiltonian Functions. Contact and Hamilto
nian Fields 152
2.3.3 Hamiltonian and Contact Distributions 153
CONTENTS vii
2.3.4 Computational Formulas. Examples 156
2.4 Lagrangian and Legendre Manifolds 160
2.4.1 General Remarks 160
2.4.2 The Basic Definitions 161
2.4.3 Nonsingular Legendre Manifolds 163
2.4.4 Representation of Arbitrary Legendre Manifolds . 166
2.4.5 Classification Lemma 171
2.5 Geometric Representation of Contact Transformations . 174
2.5.1 Nonsingular Transformations 174
2.5.2 Representation of Arbitrary Transformations . . .179
2.5.3 The Legendre Transform of an Analytic Set ... 181
2.5.4 The Composition of Contact Transformations . . 190
3 Integral Transformations of Ramified Analytic Functions 195
3.1 Integral Representations Associated with Contact Trans¬
formations 195
3.1.1 Main Definitions 195
3.1.2 Special Integral Representation 203
3.1.3 General Integral Representation 208
3.2 Integral Transformations of Homogeneous Functions . . . 212
3.2.1 Definition of the F Transformation 212
3.2.2 Action of F Transformation in Function Spaces.
The Invertibility Theorem 218
3.2.3 Commutation Formulas 223
3.3 The ^ Transformation 229
3.3.1 Definition and Basic Properties 229
3.3.2 Asymptotic Expansion of the /^ Transform of An¬
alytic Function 233
3.4 ^/^ Transformation 239
3.4.1 Definition and Commutation Formulas 239
3.4.2 Symmetrization of 3/d£ Transformation 244
4 Laplace Radon Integral Operators 251
4.1 Canonical Representations of Ramified Functions . . . .251
4.1.1 General Remarks 251
4.1.2 Local Theory 256
4.1.3 Globalization 263
viii CONTENTS
4.2 Laplace Radon Integral Operators 268
4.2.1 Motivations 268
4.2.2 Local Integral Operators and Function Spaces . . 273
4.2.3 Global Theory 277
4.2.4 Pseudodifferential Operators 281
4.3 Composition Theorems 283
4.3.1 General Formulas 283
4.3.2 Case of Pseudodifferential Operators 286
5 Cauchy Problem in Spaces of Ramified Functions 289
5.1 Equations with Constant Coefficients 289
5.1.1 Statement of the Problem 289
5.1.2 Construction of the Resolving Operator 291
5.1.3 Description of Singularities of the Solution .... 295
5.1.4 Examples of Computation of the Singularities . . 296
5.1.5 The Inhomogeneous Cauchy Problem. Reduction
to an Ordinary Differential Equation 300 ,
5.1.6 The Solution of the Reduced Equation 303
5.1.7 Verification of the Consistency Conditions . . . .309
5.1.8 Propagation of Singularities of Solutions 310
5.2 Equations with Variable Coefficients 318
5.2.1 The Cauchy Problem with Singular Initial Data .318
5.2.2 Elementary Solutions 325
5.2.3 Existence of Local Elementary Solution 328
5.3 The Characteristic Cauchy Problem 334
5.3.1 Statement of the Problem 334
5.3.2 Asymptotic Expansions of the Solution in the
Vicinity of a Noncharacteristic Point 337
5.3.3 The Construction of a Locally Trivial Stratified
Bundle 341
5.3.4 The Regularizer in the Vicinity of a Characteris¬
tic Point 354
5.3.5 Estimates for the Leading Term of Asymptotic
Expansion 359
5.3.6 Patching Solutions 368
5.4 Existence Theorems 368
5.4.1 Equations in a Bounded Domain 368
CONTENTS ix
5.4.2 A Model Example 378
5.4.3 Equations with Variable Coefficients 381
5.5 The Characteristic Cauchy Problem and Leray s Uni
formization 392
5.5.1 Statement of the Problem 392
5.5.2 Uniformization 393
5.5.3 Reduction of the Cauchy Problem 397
5.5.4 Investigation of Singularities and Asymptotic Ex¬
pansion 399
5.5.5 Leray s Uniformization and the d/d£ Formalism . 401
6 Continuation of Solutions to Elliptic Equations 405
6.1 Statement of the Problem and Review of Some Classical
Results 405
6.1.1 Motivations 405
6.1.2 Statement of the Problem 415
6.1.3 The Continuation Problem and Equations in Com¬
plex Domain 418
6.1.4 The Reflection Formula and Continuation of So¬
lutions to the Dirichlet Problem 421
6.2 The Balayage Problem 429
6.2.1 Statement of the Problem 429
6.2.2 Reduction to Cauchy Problem 430
6.2.3 Solution of the Complex Cauchy Problem .... 431
6.2.4 Solution of the Balayage Problem 433
6.2.5 A Counterexample 435
6.2.6 A Special Case 437
6.2.7 Arbitrary Equations with Constant Coefficients . 441
6.2.8 Examples 442
6.3 Reflection Formulas and Continuation of Solutions to
Boundary Value Problems 453
6.3.1 Preliminaries 453
6.3.2 Statement of the Problem 456
6.3.3 Reduction of the Basic Problem to the Problem
with a Predetermined Locus of Singularities of
the Solution 457
6.3.4 The Reflected Fundamental Solution 462
x CONTENTS
6.3.5 Properties of the Reflected Fundamental Solution 465
6.3.6 Reflection Formula and Remarks 467
6.3.7 Inhomogeneous Reflection Formula 470
Bibliography 475
Index 501
|
| any_adam_object | 1 |
| author | Sternin, Boris Ju. 1939- Šatalov, Viktor E. 1945- |
| author_GND | (DE-588)120484536 (DE-588)120484544 |
| author_facet | Sternin, Boris Ju. 1939- Šatalov, Viktor E. 1945- |
| author_role | aut aut |
| author_sort | Sternin, Boris Ju. 1939- |
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| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009929261 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:43:23Z |
| institution | BVB |
| isbn | 0792327101 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006577352 |
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| physical | XII, 504 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Sternin, Boris Ju. 1939- Verfasser (DE-588)120484536 aut Differential equations on complex manifolds by Boris Sternin and Victor Shatalov Dordrecht u.a. Kluwer Acad. Publ. 1994 XII, 504 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 276 Differential equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Komplexe Mannigfaltigkeit (DE-588)4031996-9 s DE-604 Šatalov, Viktor E. 1945- Verfasser (DE-588)120484544 aut Mathematics and its applications 276 (DE-604)BV008163334 276 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006577352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sternin, Boris Ju. 1939- Šatalov, Viktor E. 1945- Differential equations on complex manifolds Mathematics and its applications Differential equations Differentialgleichung (DE-588)4012249-9 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4031996-9 |
| title | Differential equations on complex manifolds |
| title_auth | Differential equations on complex manifolds |
| title_exact_search | Differential equations on complex manifolds |
| title_full | Differential equations on complex manifolds by Boris Sternin and Victor Shatalov |
| title_fullStr | Differential equations on complex manifolds by Boris Sternin and Victor Shatalov |
| title_full_unstemmed | Differential equations on complex manifolds by Boris Sternin and Victor Shatalov |
| title_short | Differential equations on complex manifolds |
| title_sort | differential equations on complex manifolds |
| topic | Differential equations Differentialgleichung (DE-588)4012249-9 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| topic_facet | Differential equations Differentialgleichung Komplexe Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006577352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT sterninborisju differentialequationsoncomplexmanifolds AT satalovviktore differentialequationsoncomplexmanifolds |