Approximation results by multivariate sampling Kantorovich series in Musielak-Orlicz spaces. (English) Zbl 1540.41040
Summary: In this paper we study the theory of the so-called multivariate sampling Kantorovich operators in the general frame of the Musielak-Orlicz spaces. The main result in this context is a modular convergence theorem, that can be proved by density arguments. Several concrete cases of Musielak-Orlicz spaces and of kernel functions are presented and discussed.
MSC:
| 41A35 | Approximation by operators (in particular, by integral operators) |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
sampling Kantorovich series; Musielak-Orlicz spaces; Orlicz spaces; approximation results; modular convergenceReferences:
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