Rademacher Chaoses in Problems of Constructing Spline Affine Systems


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The paper considers systems of dilations and translations of spline functions ψm 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 ψm 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 ψm constitutes a Riesz basis; moreover, lower and upper Riesz bounds for these systems can be chosen universal, i.e., independent of m.

Sobre autores

S. Lukomskii

Chernyshevskii Saratov National Research State University

Autor responsável pela correspondência
Email: lukomskiisf@info.sgu.ru
Rússia, Saratov

P. Terekhin

Chernyshevskii Saratov National Research State University

Email: lukomskiisf@info.sgu.ru
Rússia, Saratov

S. Chumachenko

Chernyshevskii Saratov National Research State University

Email: lukomskiisf@info.sgu.ru
Rússia, Saratov

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