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Zeitschrift für Analysis und ihre Anwendungen


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Volume 32, Issue 3, 2013, pp. 279–298
DOI: 10.4171/ZAA/1485

Published online: 2013-07-03

Asymptotic Formulae for Linear Combinations of Generalized Sampling Operators

Carlo Bardaro[1] and Ilaria Mantellini[2]

(1) Università degli Studi di Perugia, Italy
(2) Università degli Studi di Perugia, Italy

We give some Voronovskaja formula for linear combinations of generalized sampling operators and we furnish also a quantitative version in terms of the classical Peetre $K$-functional. This provides a better order of approximation in the asymptotic formula. We apply the general theory to various kernels: Bochner-Riesz kernel, translates of B-splines and Jackson type kernel.

Keywords: Voronovskaja-type formula, moments, generalized sampling operators, $K$-functional

Bardaro Carlo, Mantellini Ilaria: Asymptotic Formulae for Linear Combinations of Generalized Sampling Operators. Z. Anal. Anwend. 32 (2013), 279-298. doi: 10.4171/ZAA/1485