Characterization of Ultradistributional Wavefront Sets via Moritoh’s Wavelet Transform and Applications to Schrödinger Equations

Abstract

In the present paper, we employ the special wavelet transform introduced by Moritoh \cite{MO.1995} within ultradistributional spaces. Employing this wavelet transform, we define and characterise wave front sets for ultradistributions. In addition, we present several examples and determine their corresponding wave front sets. Finally, using the wavelet transform representation of the Schrödinger equation for free particles, we establish the Sobolev wave front sets of its solutions.