Conical Refraction and Higher Microlocalization

Otto Liess (auth.)9780387571058, 0-387-57105-1, 3540571051

The main topic of the book is higher analytic microlocalization and its application to problems of propagation of singularities. The part on higher microlocalization could serve as an introduction to the subject. The results on propagation refer to solutions of linear partial differentialoperators with characteristics of variable multiplicity and are of conical refraction type. The relation and interplay between these results and results or constructions from geometrical optics in crystal theory is discussed with many details. The notes are written foremost for researchers working in microlocal analysis, but it is hoped that they can also be of interest for mathematicians and physicists who work in propagation phenomena from a more classical point of view.

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Table of contents :
Introduction….Pages 1-32
Higher order wave front sets….Pages 33-93
Pseudodifferential operators….Pages 95-144
Bi-symplectic geometry and multihomogeneous maps….Pages 145-191
Fourier Integral Operators….Pages 193-223
Conical refraction, hyperbolicity and slowness surfaces….Pages 225-278
Propagation of regularity up to the boundary….Pages 279-308
Some results on transmission problems….Pages 309-345
Partial analyticity, higher microlocalization and sheaves….Pages 347-379