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Sobolev Orthogonal Systems with Two Discrete Points and Fourier Series

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Abstract

We consider the properties of systems of functions \(\Phi_1\) orthogonal with respect to a discrete-continuous Sobolev inner product of the form \(\langle f,g \rangle_S = f(a)g(a)+f(b)g(b)+\int_a^b f'(t)g'(t)dt\). In particular, we study the completeness of systems \(\Phi_1\) in the Sobolev space \(W^1_{L^2}\). Additionally, we analyze the properties of Fourier series with respect to systems \(\Phi_1\), and prove that these series converge uniformly to functions from \(W^1_{L^2}\).

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Authors and Affiliations

  1. Daghestan Federal Research Centre of the Russian Academy of Sciences, 45 M. Gadjiev str., 367000, Makhachkala, Russia

    M. G. Magomed-Kasumov

  2. Southern Mathematical Institute of the Vladikavkaz Scientific Center of Russian Academy of Sciences, 53 Vatutin str., 362027, Vladikavkaz, Russia

    M. G. Magomed-Kasumov

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  1. M. G. Magomed-Kasumov
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Correspondence to M. G. Magomed-Kasumov.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 56–66.

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Magomed-Kasumov, M.G. Sobolev Orthogonal Systems with Two Discrete Points and Fourier Series. Russ Math. 65, 47–55 (2021). https://doi.org/10.3103/S1066369X21120057

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  • DOI: https://doi.org/10.3103/S1066369X21120057

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