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This article is cited in 2 scientific papers (total 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.
Received: 25.04.2017
Citation:
S. F. Lukomskii, P. A. Terekhin, S. A. Chumachenko, “Rademacher Chaoses in Problems of Constructing Spline Affine Systems”, Mat. Zametki, 103:6 (2018), 863–874; Math. Notes, 103:6 (2018), 919–928
Linking options:
https://www.mathnet.ru/eng/mzm11654https://doi.org/10.4213/mzm11654 https://www.mathnet.ru/eng/mzm/v103/i6/p863
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Abstract page: | 379 | Full-text PDF : | 45 | References: | 37 | First page: | 24 |
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