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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 8, Pages 61–74 (Mi ivm9388)  

A criterion of convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of variation

A. Yu. Trynin

Saratov State University, 83 Astrakhanskaya str., Saratov, 410012 Russia

Abstract: We obtain a criterion of uniform convergence inside the interval $(0, \pi)$ of interpolation processes constructed from eigenfunctions of the regular Sturm–Liouville problem with a continuous potential of bounded variation. The condition of the characteristic is formulated in terms of a one-sided modulus of variations of the function.

Keywords: sinc approximation, interpolation functions, uniform approximation, Lagrange–Sturm–Liouville processes.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:8, 51–63

Bibliographic databases:

UDC: 517.518
Received: 09.06.2017

Citation: A. Yu. Trynin, “A criterion of convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 8, 61–74; Russian Math. (Iz. VUZ), 62:8 (2018), 51–63

Citation in format AMSBIB
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\by A.~Yu.~Trynin
\paper A criterion of convergence of Lagrange--Sturm--Liouville processes in terms of one-sided modulus of variation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 8
\pages 61--74
\mathnet{http://mi.mathnet.ru/ivm9388}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 8
\pages 51--63
\crossref{https://doi.org/10.3103/S1066369X1808008X}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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