The propagation of polarization for systems of transversal type
type: Item
instance of: scholarly article
title: The propagation of polarization for systems of transversal type
zbMATH Open document ID: 0856.58042
DOI: 10.1007/BF02559709
author: Niels Dencker
published in: Arkiv för Matematik
publication date: 1997-03-03T00:00:00Z
review text: The author considers systems of classical pseudodifferential operators of so-called transversal type. This means that microlocally the characteristic set is the union of two non-radial hypersurfaces, which have transversal involutive intersection at the double characteristics and, moreover, the principal symbol is of first-order on the two-dimensional kernel at the intersection. For this type of systems, the author investigates the propagation and distribution of polarization sets of solutions. The polarization set is a generalization of the wave front set and describes the components of the solution which are not smooth. The real polarizations at the double characteristic set, which by definition are limits of polarizations from outside this set, turn out to be foliated by limits of Hamiltonian orbits. The propagation of polarization is studied in this limit orbit case when the trace of the orbits satisfies a transport equation, moreover, when the polarization is transversal to the limit orbits and in the non-limit orbit case. Finally, the distributions of the polarizations in the different situations are considered.
Mathematics Subject Classification ID: 58J47
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 894901
zbMATH Keywords: polarization
zbMATH Keywords: propagation
zbMATH Keywords: transversal
zbMATH Keywords: classical pseudodifferential operator
zbMATH Keywords: wave front set
zbMATH Keywords: double characteristics
reviewed by: Walter Hoh
MaRDI profile type: Publication
cites work: On the propagation of singularities for pseudo-differential operators of principal type
cites work: On the propagation of polarization sets for systems of real principal type
cites work: On the propagation of polarization in conical refraction
cites work: The propagation of singularities for pseudo-differential operators with self-tangential characteristics
cites work: The propagation of polarization in double refraction
cites work: Preparation theorems for matrix valued functions
cites work: Microlocal structure of involutive conical refraction
cites work: Pseudo-differential operators with involutive double characteristics
description: scientific article; zbMATH DE number 894901