Localisation property of Battle-Lemari\'{e} wavelets' sums
Elena P. Ushakova, Kristina E. Ushakova
TL;DR
This paper provides explicit formulas for Battle-Lemarié wavelets and explores their localization properties, including compact support sums, with applications to characterizing certain function spaces.
Contribution
It introduces explicit formulas for Battle-Lemarié wavelets and demonstrates their localization properties and applications to norm characterization of sequence spaces.
Findings
Explicit formulas for Battle-Lemarié scaling functions and wavelets
Establishment of compactly supported sums of their translations
Application to norm characterization of sequence spaces isomorphic to Nikolskii-Besov spaces
Abstract
Explicit formulae are given for a type of Battle-Lemari\'{e} 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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