Author	Gรฅrding, Lars. author
Title	Singularities in Linear Wave Propagation [electronic resource] / by Lars Gรฅrding
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1987
Connect to	http://dx.doi.org/10.1007/BFb0073088
Descript	VI, 126 p. online resource

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

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

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Mathematics
5. Analysis