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arXiv · 1906.09946

Multiresolution expansions and wavelets in Gelfand-Shilov spaces

Stevan Pilipović·Dušan Rakić·Nenad Teofanov·Jasson Vindas
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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.

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Stevan Pilipović, Dušan Rakić, Nenad Teofanov, Jasson Vindas. 2019-06-24. Multiresolution expansions and wavelets in Gelfand-Shilov spaces. https://doi.org/10.1007/s13398-020-00789-4

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