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

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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.

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Funding

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.”

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    B. S. Kashin

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    B. S. Kashin & I. V. Limonova

  3. Laboratory “High-Dimensional Approximation and Applications,” Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia

    I. V. Limonova

Authors
  1. B. S. Kashin
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  2. I. V. Limonova
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Correspondence to B. S. Kashin.

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Kashin, B.S., Limonova, I.V. Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems. Proc. Steklov Inst. Math. 311, 152–170 (2020). https://doi.org/10.1134/S0081543820060097

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  • DOI: https://doi.org/10.1134/S0081543820060097

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