Characterization of the SG-Wave Front Set in Terms of the FBI-Transform

Abstract

The SG-wave front set, which measures microlocally the deviation of a tempered distribution from being rapidly decaying and smooth, is studied using a Fourier-Bros-Iagolnitzer transform. This generalizes the established characterization of the classical Hörmander C ∞ -wave front set. In particular, the transform used is capable of identifying singularities both at finite arguments as well as such arising at infinity.