Approximation by Nonlinear Generalized Sampling Operators of Max-Product Kind

AbstractThe aim of this note is that by using the so-called max-product methodto associate to some generalized sampling approximation linear operatorsand to the Whittaker cardinal series, nonlinear sampling operators forwhich Jackson-type approximation orders in terms of the moduli of smooth-ness are obtained. In the case of max-product Whittaker operator, forpositive valued functions, essentially a better order of approximation is ob-tained. Key words and phrases : Sampling theory, signal theory, Whittaker cardi-nal series, nonlinear generalized sampling operators of max-product kind,Jackson-type estimates. 2000 AMS Mathematics Subject Classification — Primary 94A20, 94A12,41A35; Secondary 41A25, 41A20. 1 Introduction Based on the Open Problem 5.5.4, pp. 324-326 in [11], in a series of recentpapers submitted for publication we have introduced and studied the so-calledmax-product operators attached to the Bernstein polynomials and to other linearBernstein-type operators, like those of Favard-Sz´asz-Mirakjan operators (trun-cated and nontruncated case), Baskakov operators (truncated and nontruncatedcase), Meyer-Ko¨nig and Zeller operators, and Bleimann-Butzer-Hahn operators.P This idea applied, for example, to the linear Bernstein operators B