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Full Description
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.
Contents
Higher order wave front sets.- Pseudodifferential operators.- Bi-symplectic geometry and multihomogeneous maps.- Fourier Integral Operators.- Conical refraction, hyperbolicity and slowness surfaces.- Propagation of regularity up to the boundary.- Some results on transmission problems.- Partial analyticity, higher microlocalization and sheaves.
