00-214 Jonathan Butler

Symbolic calculus and composition for pseudodifferential operators of positive and non-orthogonal type (20K, AMS-TeX) May 8, 00

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Abstract. We consider symbolic calculus and composition of $ h $ pseudodifferential operators. We define a general class of symbols and formulate natural conditions under which an $ h $ pseudodifferential operator (or $ h $ P.D.O. for short) may be represented in terms of other quantisations, and under which the composition of two $ h $ P.D.O. is an $ h $ P.D.O. The first condition corresponds, in some sense, to the $ h $ P.D.O. being of {\it positive type}, and the second to the pair of $ h $ P.D.O. being of {\it non-orthogonal} type.

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