This article is cited in 4 papers

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.

UDC: 517.518

Received: 09.06.2017

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

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