
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. Umakhanov^{ab}, I. I. Sharapudinov^{bc} ^{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
Abstract:
We consider truncated Whittaker–Kotel'nikov–Shannon operators also known as sincoperators. Conditions on continuous functions $f$ that guarantee uniform convergence of sincoperators 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 sincoperators converge uniformly to this function. In the case when $f(0)$ or $f(\pi)$ is not zero, sincoperators lose the property of uniform convergence. For example, it is well known that sincoperators have no uniform convergence to function identically equal to 1. In connection with this we introduce modified sincoperators that possess a uniform convergence property for arbitrary absolutely continuous function, satisfying Dini–Lipschitz condition.
Key words:
nonlinear system of integral equations, Hammerstein–Voltera type operator, iteration, monotonisity, primitive matrix, summerable solution.
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UDC:
517.538 Received: 03.03.2016
Citation:
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
\Bibitem{UmaSha16}
\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.
\yr 2016
\vol 18
\issue 4
\pages 6170
\mathnet{http://mi.mathnet.ru/vmj598}
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