Microlocal analysis for differential operators : an introduction /
Grigis, Alain.
Microlocal analysis for differential operators : an introduction / Alain Grigis, Johannes Sjöstrand. - Cambridge ; New York, NY : Cambridge University Press, ©1994. - 1 online resource (151 pages) : illustrations - London Mathematical Society lecture note series ; 196 . - London Mathematical Society lecture note series ; 196. .
Includes bibliographical references (pages 145-148) and indexes.
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.
9781107088566 (electronic bk.) 1107088569 (electronic bk.) 9780511721441 (electronic bk.) 0511721447 (electronic bk.) 1139884921 9781139884921 1107100518 9781107100510 1107102995 9781107102996 1107094747 9781107094741 1107091497 9781107091498
Differential operators.
Microlocal analysis.
Opérateurs différentiels.
Analyse microlocale.
MATHEMATICS--Functional Analysis.
Differential operators.
Microlocal analysis.
Pseudodifferentialoperator
Fourier-Integraloperator
Symplektische Geometrie
Lokale analyse (wiskunde)
Opérateurs différentiels.
Analyse microlocale.
Electronic books.
QA329.4 / .G75 1994eb
515/.7242
Microlocal analysis for differential operators : an introduction / Alain Grigis, Johannes Sjöstrand. - Cambridge ; New York, NY : Cambridge University Press, ©1994. - 1 online resource (151 pages) : illustrations - London Mathematical Society lecture note series ; 196 . - London Mathematical Society lecture note series ; 196. .
Includes bibliographical references (pages 145-148) and indexes.
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.
9781107088566 (electronic bk.) 1107088569 (electronic bk.) 9780511721441 (electronic bk.) 0511721447 (electronic bk.) 1139884921 9781139884921 1107100518 9781107100510 1107102995 9781107102996 1107094747 9781107094741 1107091497 9781107091498
Differential operators.
Microlocal analysis.
Opérateurs différentiels.
Analyse microlocale.
MATHEMATICS--Functional Analysis.
Differential operators.
Microlocal analysis.
Pseudodifferentialoperator
Fourier-Integraloperator
Symplektische Geometrie
Lokale analyse (wiskunde)
Opérateurs différentiels.
Analyse microlocale.
Electronic books.
QA329.4 / .G75 1994eb
515/.7242