The wavelet transforms in Gelfand-Shilov spaces
Functional Analysis
2016-08-30 v2
Abstract
We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In particular, we introduce a new family of highly time-scale localized spaces on the upper half-space. We study the wavelet synthesis operator (the left-inverse of the wavelet transform) and obtain the resolution of identity (Calder\'{o}n reproducing formula) in the context of ultradistributions.
Cite
@article{arxiv.1405.0111,
title = {The wavelet transforms in Gelfand-Shilov spaces},
author = {Stevan Pilipovic and Dusan Rakic and Nenad Teofanov and Jasson Vindas},
journal= {arXiv preprint arXiv:1405.0111},
year = {2016}
}