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Matematicheskie Zametki, 2022, Volume 111, Issue 4, Pages 561–570
DOI: https://doi.org/10.4213/mzm13321 (Mi mzm13321) 		 
On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point

M. G. Magomed-Kasumovab, T. N. Shakh-Emirovb

a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
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DOI: https://doi.org/10.4213/mzm13321
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.
Keywords: Sobolev orthogonality, completeness of orthogonal systems, representation of Sobolev systems, differentiation of Sobolev systems.
Received: 11.10.2021
Revised: 24.11.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 4, Pages 579–586
DOI: https://doi.org/10.1134/S0001434622030269
Bibliographic databases:
Document Type: Article
UDC: 517.538
Language: Russian
Citation: M. G. Magomed-Kasumov, T. N. Shakh-Emirov, “On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point”, Mat. Zametki, 111:4 (2022), 561–570; Math. Notes, 111:4 (2022), 579–586
Citation in format AMSBIB
\Bibitem{MagSha22}
\by M.~G.~Magomed-Kasumov, T.~N.~Shakh-Emirov
\paper On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 4
\pages 561--570
\mathnet{http://mi.mathnet.ru/mzm13321}
\crossref{https://doi.org/10.4213/mzm13321}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461285}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 4
\pages 579--586
\crossref{https://doi.org/10.1134/S0001434622030269}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128984269}
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