Singularities in Linear Wave Propagation
(Sprache: Englisch)
These lecture notes stemming from a course given at the Nankai Institute for Mathematics, Tianjin, in 1986 center on the construction of parametrices for fundamental solutions of hyperbolic differential and pseudodifferential operators. The greater part...
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Klappentext zu „Singularities in Linear Wave Propagation “
These lecture notes stemming from a course given at the Nankai Institute for Mathematics, Tianjin, in 1986 center on the construction of parametrices for fundamental solutions of hyperbolic differential and pseudodifferential operators. The greater part collects and organizes known material relating to these constructions. The first chapter about constant coefficient operators concludes with the Herglotz-Petrovsky formula with applications to lacunas. The rest is devoted to non-degenerate operators. The main novelty is a simple construction of a global parametrix of a first-order hyperbolic pseudodifferential operator defined on the product of a manifold and the real line. At the end, its simplest singularities are analyzed in detail using the Petrovsky lacuna edition.
Inhaltsverzeichnis zu „Singularities in Linear Wave Propagation “
- Historical introduction- Hyperbolic operators with constant coefficients
- Wave front sets and oscillatory integrals
- Pseudodifferential operators
- The Hamilton-Jacobi equation and sympletic geometry
- A global parametrix for the fundamental solution of a first order hyperbolic pseudodifferential operator
- Changes of variables and duality for general oscillatory integrals
- Sharp and diffuse fronts of paired oscillatory integrals
- References
- Index
Bibliographische Angaben
- Autor: Lars Garding
- 1987, 1987, 126 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 354018001X
- ISBN-13: 9783540180012
- Erscheinungsdatum: 10.07.1987
Sprache:
Englisch
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