Step scaling functions and the Chrestenson system

Yu. A. Farkov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 134-149.

Résumé

A review of methods for constructing step scaling functions on the positive half-line $\mathbb{R}_+$ associated with the Chrestenson functions is presented. The conditions under which such step functions generate orthogonal wavelets and tight frames are discussed. A detailed bibliography is provided.

Détail

Keywords: Walsh function, Chrestenson system, Cantor group, Vilenkin group, scaling function, wavelet, tight frame, discrete wavelet transform.
Mots-clés : Poisson formula

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