Invertibility of Microdifferential Operators of Infinite Order

Abstract

For each holomorphic microlocal operator its symbol is defined as a holomorphic function which satisfies a growth condition. A differential or micro (=pseudo-) differential operator of infinite order is naturally regarded as a holomorphic microlocal operator and its symbol coincides with the usual total symbol. Some sufficient conditions of invertibility for holomorphic microlocal operators in terms of symbols are given.