Multiresolution expansions and wavelets in Gelfand-Shilov spaces
Functional Analysis
2020-10-16 v2
Abstract
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand-Shilov spaces. Important examples of multiresolution analyses for which our results apply arise in particular from Dziuba\'{n}ski-Hern\'{a}ndez construction of band-limited wavelets with subexponential decay. Our results are twofold. Firstly, we obtain approximation properties of multiresolution expansions of Gelfand-Shilov functions and (ultra)distributions. Secondly, we establish convergence of wavelet series expansions in the same regularity framework.
Keywords
Cite
@article{arxiv.1906.09946,
title = {Multiresolution expansions and wavelets in Gelfand-Shilov spaces},
author = {Stevan Pilipović and Dušan Rakić and Nenad Teofanov and Jasson Vindas},
journal= {arXiv preprint arXiv:1906.09946},
year = {2020}
}
Comments
15 pages