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 Trudy Mat. Inst. Steklova, 2020, Volume 311, Pages 164–182 (Mi tm4117)

Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems

B. S. Kashinab, I. V. Limonovabc

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia
c Laboratory “High-Dimensional Approximation and Applications,” Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia

Abstract: For a finite orthogonal system of uniformly bounded functions, we establish the existence of sufficiently dense subsystems with the lacunarity property and a good norm estimate for the maximal partial sum operator.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.W03.31.0031 Isaac Newton Institute for Mathematical Science This work was supported by a grant of the Government of the Russian Federation (project no. 14.W03.31.0031). The first author is also grateful to the Isaac Newton Institute (Cambridge) for the support of this research within the program “Approximation, Sampling and Compression in Data Science.”

DOI: https://doi.org/10.4213/tm4117

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 311, 152–170

Bibliographic databases:

UDC: 517.5
Revised: April 7, 2020
Accepted: May 26, 2020

Citation: B. S. Kashin, I. V. Limonova, “Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 164–182; Proc. Steklov Inst. Math., 311 (2020), 152–170

Citation in format AMSBIB
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