Open Access
WINTER 2014 Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces
Danilo Costarelli, Gianluca Vinti
J. Integral Equations Applications 26(4): 455-481 (WINTER 2014). DOI: 10.1216/JIE-2014-26-4-455


In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz classes and the case of the modular approximation for functions in Orlicz spaces are considered. In the latter context, Lipschitz classes of Zygmund-type which take into account of the modular functional involved are introduced. Applications to $L^p(\R^n)$, interpolation and exponential spaces can be deduced from the general theory formulated in the setting of Orlicz spaces. The special cases of multivariate sampling Kantorovich operators based on kernels of the product type and constructed by means of Fej\'er's and B-spline kernels have been studied in details.


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Danilo Costarelli. Gianluca Vinti. "Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces." J. Integral Equations Applications 26 (4) 455 - 481, WINTER 2014.


Published: WINTER 2014
First available in Project Euclid: 9 January 2015

zbMATH: 1308.41017
MathSciNet: MR3299827
Digital Object Identifier: 10.1216/JIE-2014-26-4-455

Primary: 41A25 , 41A30 , 46E30 , 47A58 , 47B38 , 94A12

Keywords: Irregular sampling , Lipschitz classes , Multivariate sampling Kantorovich operators , order of approximation , Orlicz spaces

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 4 • WINTER 2014
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