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 ${C}^{\infty }$ 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 $\left(\Psi \right)$.

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