Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

Abstract

In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.

A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods

“…It is well-known that the operators, S w , w > 0, are approximation operators which are able to pointwise reconstruct, continuous and bounded signals, and to uniformly reconstruct, signals which are uniformly continuous and bounded, as w → +∞. Moreover, the operators S w can be used also to reconstruct not-necessarily continuous signals, e.g., signals belonging to the L p -spaces, 1 ≤ p < +∞ ( [2,3,6,7,9,10,26,32,33,41]).…”

Abstract Integration with Respect to Measures and Applications to Modular Convergence in Vector Lattice Setting

“…From the definition of l (j) , formula (13), the convergence in L 1 to 0 of (q n ) n and Axioms 2.1.a), 2.1.b), 2.1.g) it follows that |l (1) (A) − l (2) (A)| = 0, namely l (1) (A) = l (2) (A), for all A ∈ A.…”

“…In the literature there are many studies concerning the problem of approximating a real-valued function f by Urysohn-type integral operators or discrete sampling operators. These topics together with some other kind of operators, have several applications in several branches, for instance neural networks and reconstruction of signals and images (see, e.g., [1,2,[5][6][7][8][9]22,[25][26][27][28][29]).…”

Abstract integration with respect to measures and applications to modular convergence in vector lattice setting

“…From the definition of l ( j) , formula (13), the convergence in L 1 to 0 of (q n ) n and Axioms 2.1.a), 2.1.b), 2.1.g) it follows that |l (1) (A) − l (2) (A)| = 0, namely l (1) (A) = l (2) (A), for all A ∈ A . Now we define our integral for not necessarily positive functions.…”