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Classification of order preserving isomorphisms between algebras of semiclassical operators

Author: Hans Christianson
Journal: Proc. Amer. Math. Soc. 139 (2011), 499-510
MSC (2010): Primary 35S05, 58J40
Published electronically: July 15, 2010
MathSciNet review: 2736333
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Abstract: Following the work of Duistermaat and Singer on isomorphisms of algebras of global pseudodifferential operators, we classify order preserving isomorphisms of algebras of microlocally defined semiclassical pseudodifferential operators. Specifically, we show that any such isomorphism is given by conjugation by $ A = BF$, where $ B$ is a microlocally elliptic semiclassical pseudodifferential operator and $ F$ is a microlocally unitary $ h$-FIO associated to the graph of a local symplectic transformation.

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Hans Christianson
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachu- setts Avenue, Cambridge, Massachusetts 02139-4307
Address at time of publication: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250

Received by editor(s): March 6, 2008
Received by editor(s) in revised form: March 5, 2010
Published electronically: July 15, 2010
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.