Geodesic
Rademacher Chaoses in Problems of Constructing Spline Affine Systems
Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 863-874

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2018_103_6_a5,
     author = {S. F. Lukomskii and P. A. Terekhin and S. A. Chumachenko},
     title = {Rademacher {Chaoses} in {Problems} of {Constructing} {Spline} {Affine} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {863--874},
     publisher = {mathdoc},
     volume = {103},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a5/}
}
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S. F. Lukomskii; P. A. Terekhin; S. A. Chumachenko. Rademacher Chaoses in Problems of Constructing Spline Affine Systems. Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 863-874. http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a5/