Multiresolution expansions and wavelets in Gelfand–Shilov spaces
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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 Dziubański–Hernández 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.
KeywordsMultiresolution expansions Multiresolution analysis Wavelet expansions Gelfand–Shilov spaces Ultradistributions Subexponential decay
Mathematics Subject Classification42C40 46E10 46F05 46F12
S. Pilipović and N. Teofanov were supported by Serbian Ministry of Education and Science through Project 174024, project 19/6-020/961-47/18 MNRVOID of the Republic of Srpska and ANACRES. D. Rakić was supported by Serbian Ministry of Education and Science through Project III44006 and by Provincial Secretariat for Higher Education and Scientific Research through Project 142-451-2102/2019. J. Vindas was supported by Ghent University through the BOF-grants 01J11615 and 01J04017.
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