Singularities in Linear Wave Propagation / by Lars Gårding.

Format:

Book

Author/Creator:

Gårding, Lars, 1919-2014, author.

Contributor:

SpringerLink (Online service)

Series:

Nankai Institute of Mathematics, Tianjin, P.R. China ; 1241.

Nankai Institute of Mathematics, Tianjin, P.R. China ; 1241

Language:

English

Subjects (All):

Global analysis (Mathematics).

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource (VI, 126 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1987.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540472162

Access Restriction:

Restricted for use by site license.