On Local Characterization of Wave Front Sets in Terms of Boundary Values of Holomorphic Functions

Abstract

Let / be a distribution defined in an open set X in R. L. Hormander [4] introduced the notion of the analytic wave front set WFA(f) of / as a subset of the cotangent space T*(X)\0 whose projection to X coincides with the analytic singular support of /. His definition relies on the use of the Fourier transform of /. In this paper we present an alternative definition of WFA(f) in terms of boundary values of holomorphic functions which we now shortly describe. Let Q be an open subset in C. Then we shall denote by 0 (Q} the space of holomorphic functions in Q.