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/}
}
TY  - JOUR
AU  - S. F. Lukomskii
AU  - P. A. Terekhin
AU  - S. A. Chumachenko
TI  - Rademacher Chaoses in Problems of Constructing Spline Affine Systems
JO  - Matematičeskie zametki
PY  - 2018
SP  - 863
EP  - 874
VL  - 103
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a5/
LA  - ru
ID  - MZM_2018_103_6_a5
ER  - 
%0 Journal Article
%A S. F. Lukomskii
%A P. A. Terekhin
%A S. A. Chumachenko
%T Rademacher Chaoses in Problems of Constructing Spline Affine Systems
%J Matematičeskie zametki
%D 2018
%P 863-874
%V 103
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a5/
%G ru
%F MZM_2018_103_6_a5
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/

[1] B. C. Kashin, A. A. Saakyan, Ortogonalnye ryady, Izd-vo AFTs, M., 1999 | MR | Zbl

[2] J.-O. Strömberg, “A modified Franklin system and higher order spline on $\mathbb R^n$ as unconditional basis for Hardy spaces”, Conference in Harmonic Analysis in Honor of Antoni Zygmund, Vol. II, Wadsworth, Belmont, CA, 1983, 475–494 | MR

[3] G. Battle, “A block spin construction of ondelettes. I. Lemarié functions”, Comm. Math. Phys., 110:4 (1987), 601–615 | DOI | MR

[4] I. Ya. Novikov, V. Yu. Protasov, M. A. Skopina, Teoriya vspleskov, Fizmatlit, M., 2005 | MR | Zbl

[5] S. V. Astashkin, Sistema Rademakhera v funktstonalnykh prostranstvakh, Fizmatlit, M., 2017

[6] S. B. Stechkin, P. L. Ulyanov, “O mnozhestvakh edinstvennosti”, Izv. AN SSSR. Ser. matem., 26:2 (1962), 211–222 | MR | Zbl

[7] R. S. Sukhanov, “Khaosy Rademakhera i mnogochleny Bernulli”, Vestn. SamGU. Estestvennonauchn. ser., 2012, no. 3/1 (94), 66–73

[8] P. A. Terekhin, “Affinnye bazisy Rissa i dualnaya funktsiya”, Matem. sb., 207:9 (2016), 111–143 | DOI | MR | Zbl

[9] P. A. Terekhin, “Affinnye sistemy funktsii tipa Uolsha. Ortogonalizatsiya i popolnenie”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4 (1) (2014), 395–400 | Zbl

[10] S. V. Astashkin, P. A. Terekhin, “Affinnye sistemy funktsii tipa Uolsha v simmetrichnykh prostranstvakh”, Matem. sb., 209:4 (2018), 3–25 | DOI

[11] B. Granados, “Walsh wavelets”, Ann. Univ. Sci. Budapest. Sect. Comput., 13 (1992), 225–236 | MR | Zbl