Isomorphisms between Algebras of Semiclassical Pseudodifferential Operators

Hans Christianson

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arXiv · 0803.0729

Isomorphisms between Algebras of Semiclassical Pseudodifferential Operators

Hans Christianson

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Abstract

Following the work of Duistermaat-Singer \cite{DS} on isomorphisms of algebras of global pseudodifferential operators, we classify 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 microlocal $h$-FIO associated to the graph of a local symplectic transformation.

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Hans Christianson. 2008-03-05. Isomorphisms between Algebras of Semiclassical Pseudodifferential Operators. https://arxiv.org/abs/0803.0729

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