Vol. 5, No. 3, 2012

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On some microlocal properties of the range of a pseudodifferential operator of principal type

Jens Wittsten

Vol. 5 (2012), No. 3, 423–474
Abstract

We obtain microlocal analogues of results by L. Hörmander about inclusion relations between the ranges of first order differential operators with coefficients in C that fail to be locally solvable. Using similar techniques, we study the properties of the range of classical pseudodifferential operators of principal type that fail to satisfy condition (Ψ).

Keywords
pseudodifferential operators, microlocal solvability, principal type, condition ($\varPsi$), inclusion relations, bicharacteristics
Mathematical Subject Classification 2000
Primary: 35S05
Secondary: 35A07, 58J40, 47G30
Milestones
Received: 14 July 2010
Revised: 10 December 2010
Accepted: 5 February 2011
Published: 15 October 2012
Authors
Jens Wittsten
Center for Mathematical Sciences
Lund University
Box 118
SE-221 00 Lund
Sweden