Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2008
|
| Series: | Memoirs of the American Mathematical Society
906 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 194, number 906 (first of 4 numbers)." Includes bibliographical references |
| Physical Description: | VII, 134 S. |
| ISBN: | 9780821841488 |
Staff View
MARC
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| 100 | 1 | |a Ponge, Raphaël S. |d 1972- |e Verfasser |0 (DE-588)135749948 |4 aut | |
| 245 | 1 | 0 | |a Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds |c Raphaël S. Ponge |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2008 | |
| 300 | |a VII, 134 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 906 | |
| 500 | |a "Volume 194, number 906 (first of 4 numbers)." | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 4 | |a Hypoelliptic operators | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Differentiable manifolds | |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hypoelliptischer Operator |0 (DE-588)4138891-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hypoelliptischer Operator |0 (DE-588)4138891-4 |D s |
| 689 | 0 | 1 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
1.1. Heisenberg manifolds and their main differential operators 2
1.2. Intrinsic approach to the Heisenberg calculus 3
1.3. Holomorphic families of ^hDOs 8
1.4. Heat equation and complex powers of hypoelliptic operators 9
1.5. Spectral asymptotics for hypoelliptic operators 13
1.6. Weyl asymptotics and CR geometry 14
1.7. Weyl asymptotics and contact geometry 15
1.8. Organization of the memoir 15
Chapter 2. Heisenberg manifolds and their main differential operators 17
2.1. Heisenberg manifolds 17
2.2. Main differential operators on Heisenberg manifolds 22
Chapter 3. Intrinsic Approach to the Heisenberg Calculus 29
3.1. Heisenberg calculus 29
3.2. Principal symbol and model operators. 37
3.3. Hypoellipticity and Rockland condition 42
3.4. Invertibility criteria for sublaplacians 52
3.5. Invertibility criteria for the main differential operators 56
Chapter 4. Holomorphic families of hDOs 65
4.1. Almost homogeneous approach to the Heisenberg calculus 65
4.2. Holomorphic families of *ffDOs 67
4.3. Composition of holomorphic families of f/jDOs gg
4.4. Kernel characterization of holomorphic families of l DOs 73
4.5. Holomorphic families of *DOs on a general Heisenberg manifold 76
4.6. Transposes and adjoints of holomorphic families of fffDOs 78
Chapter 5. Heat Equation and Complex Powers of Hypoelliptic Operators 81
5.1. Pseudodifferential representation of the heat kernel 81
5.2. Heat equation and sublaplacians 87
5.3. Complex powers of hypoelliptic differential operators 93
5.4. Rockland condition and the heat equation 97
5.5. Weighted Sobolev Spaces 102
Chapter 6. Spectral Asymptotics for Hypoelliptic Operators 107
6.1. Spectral asymptotics for hypoelliptic operators 107
6.2. Weyl asymptotics and CR geometry 111
6.3. Weyl asymptotics and contact geometry 119
V
vi CONTENTS
Appendix A. Proof of Proposition 3.1.18 123
Appendix B. Proof of Proposition 3.1.21 127
Appendix. Bibliography 131
References 131
|
| adam_txt |
Contents
Chapter 1. Introduction 1
1.1. Heisenberg manifolds and their main differential operators 2
1.2. Intrinsic approach to the Heisenberg calculus 3
1.3. Holomorphic families of ^hDOs 8
1.4. Heat equation and complex powers of hypoelliptic operators 9
1.5. Spectral asymptotics for hypoelliptic operators 13
1.6. Weyl asymptotics and CR geometry 14
1.7. Weyl asymptotics and contact geometry 15
1.8. Organization of the memoir 15
Chapter 2. Heisenberg manifolds and their main differential operators 17
2.1. Heisenberg manifolds 17
2.2. Main differential operators on Heisenberg manifolds 22
Chapter 3. Intrinsic Approach to the Heisenberg Calculus 29
3.1. Heisenberg calculus 29
3.2. Principal symbol and model operators. 37
3.3. Hypoellipticity and Rockland condition 42
3.4. Invertibility criteria for sublaplacians 52
3.5. Invertibility criteria for the main differential operators 56
Chapter 4. Holomorphic families of \ hDOs 65
4.1. Almost homogeneous approach to the Heisenberg calculus 65
4.2. Holomorphic families of *ffDOs 67
4.3. Composition of holomorphic families of 'f/jDOs gg
4.4. Kernel characterization of holomorphic families of l DOs 73
4.5. Holomorphic families of *DOs on a general Heisenberg manifold 76
4.6. Transposes and adjoints of holomorphic families of \fffDOs 78
Chapter 5. Heat Equation and Complex Powers of Hypoelliptic Operators 81
5.1. Pseudodifferential representation of the heat kernel 81
5.2. Heat equation and sublaplacians 87
5.3. Complex powers of hypoelliptic differential operators 93
5.4. Rockland condition and the heat equation 97
5.5. Weighted Sobolev Spaces 102
Chapter 6. Spectral Asymptotics for Hypoelliptic Operators 107
6.1. Spectral asymptotics for hypoelliptic operators 107
6.2. Weyl asymptotics and CR geometry 111
6.3. Weyl asymptotics and contact geometry 119
V
vi CONTENTS
Appendix A. Proof of Proposition 3.1.18 123
Appendix B. Proof of Proposition 3.1.21 127
Appendix. Bibliography 131
References 131 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:13:29Z |
| indexdate | 2024-07-09T21:17:08Z |
| institution | BVB |
| isbn | 9780821841488 |
| language | English |
| lccn | 2008008508 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016556751 |
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| physical | VII, 134 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Ponge, Raphaël S. 1972- Verfasser (DE-588)135749948 aut Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds Raphaël S. Ponge Providence, R.I. American Mathematical Society 2008 VII, 134 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 906 "Volume 194, number 906 (first of 4 numbers)." Includes bibliographical references Hypoelliptic operators Spectral theory (Mathematics) Calculus Differentiable manifolds Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Hypoelliptischer Operator (DE-588)4138891-4 gnd rswk-swf Hypoelliptischer Operator (DE-588)4138891-4 s Spektraltheorie (DE-588)4116561-5 s DE-604 Memoirs of the American Mathematical Society 906 (DE-604)BV008000141 906 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016556751&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ponge, Raphaël S. 1972- Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds Memoirs of the American Mathematical Society Hypoelliptic operators Spectral theory (Mathematics) Calculus Differentiable manifolds Spektraltheorie (DE-588)4116561-5 gnd Hypoelliptischer Operator (DE-588)4138891-4 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4138891-4 |
| title | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds |
| title_auth | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds |
| title_exact_search | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds |
| title_exact_search_txtP | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds |
| title_full | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds Raphaël S. Ponge |
| title_fullStr | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds Raphaël S. Ponge |
| title_full_unstemmed | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds Raphaël S. Ponge |
| title_short | Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds |
| title_sort | heisenberg calculus and spectral theory of hypoelliptic operators on heisenberg manifolds |
| topic | Hypoelliptic operators Spectral theory (Mathematics) Calculus Differentiable manifolds Spektraltheorie (DE-588)4116561-5 gnd Hypoelliptischer Operator (DE-588)4138891-4 gnd |
| topic_facet | Hypoelliptic operators Spectral theory (Mathematics) Calculus Differentiable manifolds Spektraltheorie Hypoelliptischer Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016556751&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT pongeraphaels heisenbergcalculusandspectraltheoryofhypoellipticoperatorsonheisenbergmanifolds |