Microlocal analysis for differential operators: an introduction
This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emp...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1994
|
| Series: | London Mathematical Society lecture note series
196 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (151 pages) |
| ISBN: | 9780511721441 |
| DOI: | 10.1017/CBO9780511721441 |
Staff View
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| 505 | 8 | |a 1. Symbols and oscillatory integrals -- 2. The method of stationary phase -- 3. Pseudodifferential operators -- 4. Application to elliptic operators and L[superscript 2] continuity -- 5. Local symplectic geometry I (Hamilton-Jacobi theory) -- 6. The strictly hyperbolic Cauchy problem construction of a parametrix -- 7. The wavefront set (singular spectrum) of a distribution -- 8. Propagation of singularities for operators of real principle type -- 9. Local symplectic geometry II -- 10. Canonical transformations of pseudodifferential operators -- 11. Global theory of Fourier integral operators -- 12. Spectral theory for elliptic operators | |
| 520 | |a This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature | ||
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| author | Grigis, Alain |
| author_facet | Grigis, Alain |
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| bvnumber | BV043942259 |
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| contents | 1. Symbols and oscillatory integrals -- 2. The method of stationary phase -- 3. Pseudodifferential operators -- 4. Application to elliptic operators and L[superscript 2] continuity -- 5. Local symplectic geometry I (Hamilton-Jacobi theory) -- 6. The strictly hyperbolic Cauchy problem construction of a parametrix -- 7. The wavefront set (singular spectrum) of a distribution -- 8. Propagation of singularities for operators of real principle type -- 9. Local symplectic geometry II -- 10. Canonical transformations of pseudodifferential operators -- 11. Global theory of Fourier integral operators -- 12. Spectral theory for elliptic operators |
| ctrlnum | (ZDB-20-CBO)CR9780511721441 (OCoLC)967776361 (DE-599)BVBBV043942259 |
| 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 47242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511721441 |
| format | Electronic eBook |
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| id | DE-604.BV043942259 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511721441 |
| language | English |
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| publisher | Cambridge University Press |
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| spelling | Grigis, Alain Verfasser aut Microlocal analysis for differential operators an introduction Alain Grigis, Johannes Sjöstrand Cambridge Cambridge University Press 1994 1 online resource (151 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 196 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Symbols and oscillatory integrals -- 2. The method of stationary phase -- 3. Pseudodifferential operators -- 4. Application to elliptic operators and L[superscript 2] continuity -- 5. Local symplectic geometry I (Hamilton-Jacobi theory) -- 6. The strictly hyperbolic Cauchy problem construction of a parametrix -- 7. The wavefront set (singular spectrum) of a distribution -- 8. Propagation of singularities for operators of real principle type -- 9. Local symplectic geometry II -- 10. Canonical transformations of pseudodifferential operators -- 11. Global theory of Fourier integral operators -- 12. Spectral theory for elliptic operators This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature Differential operators Microlocal analysis Differentialoperator (DE-588)4012251-7 gnd rswk-swf Mikrolokale Analysis (DE-588)4169832-0 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s Mikrolokale Analysis (DE-588)4169832-0 s 1\p DE-604 Sjöstrand, J. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-44986-1 https://doi.org/10.1017/CBO9780511721441 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grigis, Alain Microlocal analysis for differential operators an introduction 1. Symbols and oscillatory integrals -- 2. The method of stationary phase -- 3. Pseudodifferential operators -- 4. Application to elliptic operators and L[superscript 2] continuity -- 5. Local symplectic geometry I (Hamilton-Jacobi theory) -- 6. The strictly hyperbolic Cauchy problem construction of a parametrix -- 7. The wavefront set (singular spectrum) of a distribution -- 8. Propagation of singularities for operators of real principle type -- 9. Local symplectic geometry II -- 10. Canonical transformations of pseudodifferential operators -- 11. Global theory of Fourier integral operators -- 12. Spectral theory for elliptic operators Differential operators Microlocal analysis Differentialoperator (DE-588)4012251-7 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| subject_GND | (DE-588)4012251-7 (DE-588)4169832-0 |
| title | Microlocal analysis for differential operators an introduction |
| title_auth | Microlocal analysis for differential operators an introduction |
| title_exact_search | Microlocal analysis for differential operators an introduction |
| title_full | Microlocal analysis for differential operators an introduction Alain Grigis, Johannes Sjöstrand |
| title_fullStr | Microlocal analysis for differential operators an introduction Alain Grigis, Johannes Sjöstrand |
| title_full_unstemmed | Microlocal analysis for differential operators an introduction Alain Grigis, Johannes Sjöstrand |
| title_short | Microlocal analysis for differential operators |
| title_sort | microlocal analysis for differential operators an introduction |
| title_sub | an introduction |
| topic | Differential operators Microlocal analysis Differentialoperator (DE-588)4012251-7 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| topic_facet | Differential operators Microlocal analysis Differentialoperator Mikrolokale Analysis |
| url | https://doi.org/10.1017/CBO9780511721441 |
| work_keys_str_mv | AT grigisalain microlocalanalysisfordifferentialoperatorsanintroduction AT sjostrandj microlocalanalysisfordifferentialoperatorsanintroduction |