Lagrangian manifolds and the Maslov operator:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1990
|
| Series: | Springer series in Soviet mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 395 S. |
| ISBN: | 3540136134 0387136134 |
Staff View
MARC
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| 100 | 1 | |a Miščenko, Aleksandr S. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Lagranževy mnogoobrazija i metod kanoničeskogo operatora |
| 245 | 1 | 0 | |a Lagrangian manifolds and the Maslov operator |c A. S. Mishchenko ; V. E. Shatalov ; B. Yu. Sternin. Transl. from the Russian by Dana Mackenzie |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1990 | |
| 300 | |a X, 395 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Springer series in Soviet mathematics | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Introduction 1
Part I. The Topology of Lagrangian Manifolds
Chapter 1. Some Topological Considerations 33
1.1 Manifolds and Bundles 33
1.2 Theorems on Transversal Regularity 67
1.3 The Index of Intersection of Submanifolds 79
1.4 Homotopy Groups 86
Chapter 2. The Geometry of Real Lagrangian Manifolds 89
2.1 Lagrangian Manifolds in Hamiltonian Space 89
2.2 The Cohomology of the Lagrangian Grassmannian 94
2.3 Characteristic Classes of Lagrangian Manifolds 104
2.4 Lagrangian Manifolds in General Position 110
Chapter 3. Complex Lagrangian Manifolds 116
3.1 The Grassmannian of Positive Lagrangian Planes 116
3.2 The Maslov Index of Complex Lagrangian Manifolds 124
3.3 Analysis on s Analytic Manifolds 137
3.4 Positive Lagrangian s Analytic Manifolds 169
Part II. Maslov s Canonical Operator on a Real Lagrangian Manifold
Chapter 4. Maslov s Canonical Operator (Real Case) 183
4.1 The Construction of Maslov s Elementary Canonical Operator . 183
4.2 Commutation of Maslov s Canonical Operator and the
Hamiltonian Operator 196
Chapter 5. The Asymptotics of Integrals of Rapidly Oscillating
Functions with a Complex Phase 208
5.1 The Formula for Asymptotic Expansion of the Integral
of a Rapidly Oscillating Function 209
x Table of Contents
5.2 Proof of Proposition 1.2 215
Chapter 6. Maslov s Canonical Operator (Complex Case) 232
6.1 Maslov s Elementary Operator on a Complex Lagrangian
Manifold 232
6.2 Commutation of the Canonical Operator and the Hamiltonian
(Elementary Theory) 241
6.3 Commutation of Maslov s Canonical Operator and the
Hamiltonian (General Theory) 246
6.4 Other Approaches 258
6.5 Appendix. The 1/h Fouiier Transform 265
Chapter 7. Some Applications 268
7.1 Asymptotic Solutions of the Cauchy Problem 268
7.2 Asymptotics of the Spectrum of 1/h Pseudodifferential Operators 279
7.3 Systems of Equations 301
Appendix. Fourier Maslov Integral Operators (The Smooth Theory
of Maslov s Canonical Operator)
by V.E. Nazaikinskij, V.G. Oshchmian, B.Yu. Sternin,
and V.E. Shatalov 307
Bibliography 377
Notation Index 391
Subject Index 393
|
| any_adam_object | 1 |
| author | Miščenko, Aleksandr S. Šatalov, Viktor E. 1945- Sternin, Boris Ju. 1939- |
| author_GND | (DE-588)120484544 (DE-588)120484536 |
| author_facet | Miščenko, Aleksandr S. Šatalov, Viktor E. 1945- Sternin, Boris Ju. 1939- |
| author_role | aut aut aut |
| author_sort | Miščenko, Aleksandr S. |
| author_variant | a s m as asm v e š ve veš b j s bj bjs |
| building | Verbundindex |
| bvnumber | BV002440991 |
| classification_rvk | SK 350 SK 540 SK 620 |
| classification_tum | PHY 013f MAT 470f |
| ctrlnum | (OCoLC)246751596 (DE-599)BVBBV002440991 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV002440991 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:45:15Z |
| institution | BVB |
| isbn | 3540136134 0387136134 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001582564 |
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| physical | X, 395 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in Soviet mathematics |
| spelling | Miščenko, Aleksandr S. Verfasser aut Lagranževy mnogoobrazija i metod kanoničeskogo operatora Lagrangian manifolds and the Maslov operator A. S. Mishchenko ; V. E. Shatalov ; B. Yu. Sternin. Transl. from the Russian by Dana Mackenzie Berlin u.a. Springer 1990 X, 395 S. txt rdacontent n rdamedia nc rdacarrier Springer series in Soviet mathematics Lagrange-Mannigfaltigkeit (DE-588)4212799-3 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf Kanonischer Maslov-Operator (DE-588)4254844-5 gnd rswk-swf Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf Pseudodifferentialgleichung (DE-588)4121533-3 gnd rswk-swf Lagrange-Mannigfaltigkeit (DE-588)4212799-3 s Pseudodifferentialgleichung (DE-588)4121533-3 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s Kanonischer Maslov-Operator (DE-588)4254844-5 s DE-604 Pseudodifferentialoperator (DE-588)4047640-6 s Asymptotische Entwicklung (DE-588)4112609-9 s Šatalov, Viktor E. 1945- Verfasser (DE-588)120484544 aut Sternin, Boris Ju. 1939- Verfasser (DE-588)120484536 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001582564&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miščenko, Aleksandr S. Šatalov, Viktor E. 1945- Sternin, Boris Ju. 1939- Lagrangian manifolds and the Maslov operator Lagrange-Mannigfaltigkeit (DE-588)4212799-3 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd Kanonischer Maslov-Operator (DE-588)4254844-5 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Pseudodifferentialgleichung (DE-588)4121533-3 gnd |
| subject_GND | (DE-588)4212799-3 (DE-588)4112609-9 (DE-588)4047640-6 (DE-588)4254844-5 (DE-588)4134367-0 (DE-588)4121533-3 |
| title | Lagrangian manifolds and the Maslov operator |
| title_alt | Lagranževy mnogoobrazija i metod kanoničeskogo operatora |
| title_auth | Lagrangian manifolds and the Maslov operator |
| title_exact_search | Lagrangian manifolds and the Maslov operator |
| title_full | Lagrangian manifolds and the Maslov operator A. S. Mishchenko ; V. E. Shatalov ; B. Yu. Sternin. Transl. from the Russian by Dana Mackenzie |
| title_fullStr | Lagrangian manifolds and the Maslov operator A. S. Mishchenko ; V. E. Shatalov ; B. Yu. Sternin. Transl. from the Russian by Dana Mackenzie |
| title_full_unstemmed | Lagrangian manifolds and the Maslov operator A. S. Mishchenko ; V. E. Shatalov ; B. Yu. Sternin. Transl. from the Russian by Dana Mackenzie |
| title_short | Lagrangian manifolds and the Maslov operator |
| title_sort | lagrangian manifolds and the maslov operator |
| topic | Lagrange-Mannigfaltigkeit (DE-588)4212799-3 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd Kanonischer Maslov-Operator (DE-588)4254844-5 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Pseudodifferentialgleichung (DE-588)4121533-3 gnd |
| topic_facet | Lagrange-Mannigfaltigkeit Asymptotische Entwicklung Pseudodifferentialoperator Kanonischer Maslov-Operator Asymptotisches Lösungsverhalten Pseudodifferentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001582564&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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