Kantorovich-Type Generalized Sampling Series in the Setting of Orlicz Spaces

Boundedness properties of semi-discrete sampling operators in Mellin–Lebesgue spaces

“…It is defined, in a generalized form, by (see [11], and [15] for the Fourier version) We have J γ,β ∈ Φ ∩ Ψ ∩ X p 0 for any p ∈ [1, ∞]. 4.…”

“…A further interesting modification of the generalized sampling series is given by the Kantorovich sampling operator, introduced in [15]. In this operator the sampled values of the signal are replaced by an integral mean between two sample points (not necessarily equally spaced over the real line).…”

Enhancement of Cone-Beam Computed Tomography Dental-Maxillofacial Images by Sampling Kantorovich Algorithm

“…The SK operators have been introduced in [1] in a one-dimensional setting, and subsequently, they have been extended to the multivariate frame in [2]. The SK operators (based upon non-negative kernels) belong to the wide family of linear (positive) operators, which is one of the most studied topics in approximation theory (see, e.g., [3][4][5][6][7]).…”

A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces

“…The sampling Kantorovich operators S w have been introduced by Bardaro, Butzer, Stens and Vinti in [8], in order to study an L 1 -version of the so-called generalized sampling operators ( [12,32,14]). The main peculiarity of the sampling Kantorovich operators is that they revealed to be suitable in order to reconstruct not necessarily continuous signals ( [2]).…”

“…Indeed, in the original paper [8] the authors proved the modular convergence of the operators S w in the general setting of Orlicz spaces, which include, as a special case, the L p -spaces.…”