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On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point

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Abstract

We obtain the representation of systems of functions \(\Phi_1\) orthogonal with respect to the Sobolev-type inner product with one discrete point in terms of functions of systems orthogonal in \(L^2\). Questions relating to the completeness of the system \(\Phi_1\) are investigated. Some properties of systems of functions obtained by differentiating the system \(\Phi_1\) are studied.

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References

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Authors and Affiliations

  1. Southern Mathematical Institute of Vladikavkaz Scientific Center of Russian Academy of Sciences, Vladikavkaz, 362027, Russia

    M. G. Magomed-Kasumov

  2. Daghestan Federal Research Center of Russian Academy of Sciences, Makhachkala, 367000, Russia

    M. G. Magomed-Kasumov & T. N. Shakh-Émirov

Authors
  1. M. G. Magomed-Kasumov
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  2. T. N. Shakh-Émirov
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Correspondence to M. G. Magomed-Kasumov.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 561-570 https://doi.org/10.4213/mzm13321.

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Magomed-Kasumov, M.G., Shakh-Émirov, T.N. On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point. Math Notes 111, 579–586 (2022). https://doi.org/10.1134/S0001434622030269

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  • DOI: https://doi.org/10.1134/S0001434622030269

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