Geodesic
Step scaling functions and the Chrestenson system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 134-149

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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.
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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     author = {Yu. A. Farkov},
     title = {Step scaling functions and the {Chrestenson} system},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {225},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2023_225_a11/}
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Yu. A. Farkov. Step scaling functions and the Chrestenson system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 134-149. http://geodesic.mathdoc.fr/item/INTO_2023_225_a11/