Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces
By Danilo Costarelli, Gianluca Vinti. 2014
80 citations recorded by the source corpus.
In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of the 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 Lp(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 Fejer's and B-spline kernels have been studied in details.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f025aaba562cd20954f8f4450edc56228deb2c0f
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Citations in the corpus
- Approximation of discontinuous signals by sampling Kantorovich series (2015, methodology): “[8, 27, 28, 29], both for functions of one and several variables.”
- An Inverse Result of Approximation by Sampling Kantorovich Series (2018, background): “[21,22,37]), their behaviour at the discontinuity points of a given signal (see [26]), and so on.”
- A characterization of the convergence in variation for the generalized sampling series (2017, unknown): “of Section 2) based on the kernel χ (see [10, 19]).”
- Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces (2015, background): “The symbol means that, for any two functions f , g : n → , f (t) = (g (t)) as ‖t‖2 → 0, if there exist constants C , > 0 such that ∣∣f (t)∣∣ ≤ C ∣∣g (t)∣∣ for every t ∈ n , with ‖t‖2 ≤ ([12, 36]).”