Classification of order preserving isomorphisms between algebras of semiclassical operators
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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.References
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Additional Information
- 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
- MR Author ID: 695231
- Email: hans@math.mit.edu
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 499-510
- MSC (2010): Primary 35S05, 58J40
- DOI: https://doi.org/10.1090/S0002-9939-2010-10481-1
- MathSciNet review: 2736333