General Theory of Global Smoothness Preservation by Multivariate 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 17 in Approximation Theory, 2000, pp 429-450 from Springer

Abstract: Abstract This is a continuation and generalization in the multivariate case of Chapter 16. Namely, by using various kinds of multivariate moduli of smoothness, in this chapter is presented that the multivariate variants of the well-known singular integrals of Picard, Poisson-Cauchy, Gauss-Weierstrass and their Jackson type generalizations satisfy the “global smoothness preservation” property. Here we follow the basic study done by both authors [27].

Keywords: General Theory; General Result; Basic Study; Approximation Theory; Singular Integral (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_17

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DOI: 10.1007/978-1-4612-1360-4_17

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