Singularities in Linear Wave Propagation

Lars Garding

ISBN 10: 354018001X / ISBN 13: 9783540180012

Editore: Springer Berlin Heidelberg, 1987

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783540180012

Dati bibliografici

• Titolo: Singularities in Linear Wave Propagation
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 1987
• Lingua: Inglese
• ISBN 10: 354018001X
• ISBN 13: 9783540180012
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 8 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 8 millimetri di profondità
• Peso: 213 grammi

Descrizione articolo

Riassunto

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.

Contenuti

Singularities in linear wave propagation.- Hyperbolic operators with constant coefficients.- Wave front sets and oscillatory integrals.- Pseudodifferential operators.- The Hamilton-Jacobi equation and symplectic 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.