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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 260, Pages 44–56 (Mi tm585)  
This article is cited in 2 scientific papers (total in 2 papers)

A Generalization of Kolmogorov's Theorem to Biorthogonal Systems

S. V. Bochkarev

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (200 kB) Citations (2)
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Abstract: The fundamental Kolmogorov's theorem about divergent trigonometric Fourier series is generalized to bounded biorthonormal systems defined on a separable metric space with Borel regular outer measure. Sharp lower bounds at points and on sets of positive measure are obtained for the arithmetic means of the symmetrized Lebesgue functions of biorthonormal systems defined on an arbitrary measure space. Earlier, similar results were obtained by the author for orthogonal systems on an interval.
Received in September 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 260, Pages 37–49
DOI: https://doi.org/10.1134/S0081543808010045
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 44–56; Proc. Steklov Inst. Math., 260 (2008), 37–49
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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