Extract
Kantorovich-type generalized sampling series in the setting of Orlicz spaces.
Abstract
This paper deals with the Kantorovich version of generalized sampling series, the first one to be primarily concerned with this version. It is devoted to the study of these series in Orlicz spaces, L[phi](R), in the instance of irregularly spaced samples. A modular convergence theorem for functions f [member of] L [delta] (R) is deduced. The convergence in [L.sup.p] (R)-space, L log L-space, and exponential spaces follow as particular results. Applications are given to several sampling series with special kernels, especially in the instance of discontinuous signals. Graphical representations for the various examples are included. 2000 AMS Mathematics Subject Classification: 41A25, 41A35, 46E30, 47A58, 47B38, 94A12 Key words and phrases: Generalized sampling operators, Kantorovich-type operators, irregular sampling, Orlicz spaces, L log L-space, modular convergence 1 Introduction Whereas the Bernstein polynomials [B.sub.n]f are kn...See the full content of this document
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