Localisation property of Battle–Lemarié wavelets' sums

Explicit formulae are given for a type of Battle–Lemarié scaling functions and related wavelets. Compactly supported sums of their translations are established and applied to alternative norm characterization of sequence spaces isometrically isomorphic to Nikolskii–Besov spaces on R.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-05, Vol.461 (1), p.176-197
Main Authors: Ushakova, Elena P., Ushakova, Kristina E.
Format: Article
Language:English
Subjects:
B-spline
Battle–Lemarié scaling function and wavelet
Construction
Localisation
Nikolskii–Besov spaces
Spline wavelet
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Description
Summary:Explicit formulae are given for a type of Battle–Lemarié scaling functions and related wavelets. Compactly supported sums of their translations are established and applied to alternative norm characterization of sequence spaces isometrically isomorphic to Nikolskii–Besov spaces on R.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.12.066