Journal of Integral Equations and Applications

Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces

Danilo Costarelli and Gianluca Vinti

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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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J. Integral Equations Applications, Volume 26, Number 4 (2014), 455-481.

First available in Project Euclid: 9 January 2015

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Primary: 41A25: Rate of convergence, degree of approximation 41A30: Approximation by other special function classes 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47A58: Operator approximation theory 47B38: Operators on function spaces (general) 94A12: Signal theory (characterization, reconstruction, filtering, etc.)

Multivariate sampling Kantorovich operators Orlicz spaces order of approximation Lipschitz classes irregular sampling


Costarelli, Danilo; Vinti, Gianluca. Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces. J. Integral Equations Applications 26 (2014), no. 4, 455--481. doi:10.1216/JIE-2014-26-4-455.

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