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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 1430–1442
DOI: https://doi.org/doi.org/10.33048/semi.2023.20.088 (Mi semr1651) 		 
Real, complex and functional analysis

Stability condition and Riesz bounds for exponential splines

E. V. Mishchenko

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
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DOI: https://doi.org/doi.org/10.33048/semi.2023.20.088
Abstract: Stability of the family of integer translations of exponential spline $U_{m,p}$ for arbitrary $m,p$ is proven; Riesz bounds are determined. The method presented in the paper allows to calculate Riesz bounds for the convolution of a B-spline of an arbitrary order and a function with an appropriated Fourier transform.
Keywords: E-spline, Riesz basis, Riesz bounds, functional series.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0008
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).
Received January 16, 2023, published December 12, 2023
Document Type: Article
UDC: 517.518.34, 517.521.1
MSC: 46B15, 40A30
Language: Russian
Citation: E. V. Mishchenko, “Stability condition and Riesz bounds for exponential splines”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 1430–1442
Citation in format AMSBIB
\Bibitem{Mis23}
\by E.~V.~Mishchenko
\paper Stability condition and Riesz bounds for exponential splines
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 1430--1442
\mathnet{http://mi.mathnet.ru/semr1651}
\crossref{https://doi.org/doi.org/10.33048/semi.2023.20.088}
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