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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2023 Volume 225, Pages 134–149 (Mi into1194)

This article is cited in 1 paper

Step scaling functions and the Chrestenson system

Yu. A. Farkov

Russian Academy of National Economy and Public Administration under the President of the Russian Federation, Moscow

Abstract: 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, Poisson formula, Cantor group, Vilenkin group, scaling function, wavelet, tight frame, discrete wavelet transform.

UDC: 517.518

MSC: 42C15,42C40,43A15,65T60

DOI: 10.36535/0233-6723-2023-225-134-149



© Steklov Math. Inst. of RAS, 2025