Rademacher Chaoses in Problems of Constructing Spline Affine Systems

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 $m$.