Singularities in linear wave propagation
By: Lars Gårding.
Series: Lecture notes in mathematics ;; 1241; Lecture notes in mathematics (Springer-Verlag) ;; 1241.
Publisher: Springer-Verlag
Published: 1987
Place of publication: Berlin; New York
Language: eng
Number of pages: 123
Subjects: Differential equations, Hyperbolic.; Wave motion, Theory of.; Singularities (Mathematics)
Description: 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.
Notes: Includes bibliographical references and index.
"Subseries: Nankai Institute of Mathematics, Tianjin, P.R. China, vol. 2."