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

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.