Rademacher Chaoses in Problems of Constructing Spline Affine Systems

Abstract

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