General Theory of Global Smoothness Preservation by Univariate Singular Operators

George A. Anastassiou and Sorin G. Gal
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George A. Anastassiou: University of Memphis, Department of Mathematical Sciences
Sorin G. Gal: University of Oradea, Department of Mathematics

Chapter 16 in Approximation Theory, 2000, pp 401-427 from Springer

Abstract: Abstract In this chapter we show that the well-known singular integrals of Picard, Poisson-Cauchy, Gauss-Weierstrass and their Jackson type generalizations satisfy the “global smoothness preservation” property. I.e., they “ripple” less than the function they are applied on, that is producing a nice and fit approximation to the unit. The related results are given over various spaces of functions and the associated inequalities involve different types of corresponding moduli of smoothness. Several times these inequalities are proved to be sharp, namely they are attained. Here we follow the basic study done by both authors [26].

Keywords: General Theory; Singular Integral; Singular Integral Operator; Positive Linear Operator; Singular Operator (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1360-4_16

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DOI: 10.1007/978-1-4612-1360-4_16

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