This article is cited in 2 papers

Rademacher Chaoses in Problems of Constructing Spline Affine Systems

S. F. Lukomskii, P. A. Terekhin, S. A. Chumachenko

Saratov State University

Abstract: The paper considers systems of dilations and translations of spline functions $\psi_m$ each of which is obtained by successive integration and antiperiodization of the previous one and the initial function is the Haar function $\chi$. It is proved that, first, each such function $\psi_m$ is the sum of finitely many series in Rademacher chaoses of odd order and, second, for each $m$, the system of dilations and translations of the function $\psi_m$ constitutes a Riesz basis; moreover, lower and upper Riesz bounds for these systems can be chosen universal, i.e., independent of $m$.

Keywords: Rademacher functions, Rademacher chaos, Haar system, system of dilations and translations, splines, Riesz basis, Riesz bounds.

UDC: 517.51

Received: 25.04.2017

DOI: 10.4213/mzm11654

 English version: Mathematical Notes, 2018, 103:6, 919–928

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