This article is cited in 4 scientific papers (total in 4 papers)
Interpolation of functions by the Whittaker sums and their modifications: conditions for uniform convergence
A. Y. Umakhanovab, I. I. Sharapudinovbc
a Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
b Daghestan State Pedagogical University
c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences
We consider truncated Whittaker–Kotel'nikov–Shannon operators also known as sinc-operators. Conditions on continuous functions $f$ that guarantee uniform convergence of sinc-operators to such functions are obtained. It is shown that if a function is absolutely continuous, satisfies Dini–Lipschitz condition and vanishes at the end of the segment $[0,\pi]$, then sinc-operators converge uniformly to this function. In the case when $f(0)$ or $f(\pi)$ is not zero, sinc-operators lose the property of uniform convergence. For example, it is well known that sinc-operators have no uniform convergence to function identically equal to 1. In connection with this we introduce modified sinc-operators that possess a uniform convergence property for arbitrary absolutely continuous function, satisfying Dini–Lipschitz condition.
nonlinear system of integral equations, Hammerstein–Voltera type operator, iteration, monotonisity, primitive matrix, summerable solution.
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A. Y. Umakhanov, I. I. Sharapudinov, “Interpolation of functions by the Whittaker sums and their modifications: conditions for uniform convergence”, Vladikavkaz. Mat. Zh., 18:4 (2016), 61–70
Citation in format AMSBIB
\by A.~Y.~Umakhanov, I.~I.~Sharapudinov
\paper Interpolation of functions by the Whittaker sums and their modifications: conditions for uniform convergence
\jour Vladikavkaz. Mat. Zh.
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