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Multiresolution expansions and wavelets in Gelfand-Shilov spaces

Journal Contribution - Journal Article

We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of GelfandU+2013Shilov spaces. Important examples of multiresolution analyses for which our results apply arise in particular from DziubanskiU+2013HernĂ¡ndez construction of band-limited wavelets with subexponential decay. Our results are twofold. Firstly, we obtain approximation properties of multiresolution expansions of GelfandU+2013Shilov functions and (ultra)distributions. Secondly, we establish convergence of wavelet series expansions in the same regularity framework.
Journal: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
ISSN: 1579-1505
Issue: 2
Volume: 114
Accessibility:Open