Global smoothness preservation by singular integrals

Global smoothness preservation and simultaneous approximation by multivariate discrete operators

In this article we study the multivariate generalized discrete singular operators defined on R , N ≥ 1, regarding their simultaneus global smoothness preservation property with respect to Lp norm for 1 ≤ p ≤ ∞, by using higher order moduli of smoothness. Furthermore, we study their simultaneous approximation properties. Mathematics Subject Classification (2010): 26A15, 26D15, 41A17, 41A25, 41A2...

Approximation theory - moduli of continuity and global smoothness preservation

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Singular Integrals

In this paper I will a t tempt to describe the subject as it has developed in the last fifteen years, outlining the methods by which its problems have been approached and discussing its connections with other branches of Analysis. I t will perhaps be best to start by considering certain classical situations which lead naturally to singular integrals and which contain the seeds of some of the me...

Multi-parameter singular integrals

Evaluating Singular and Nearly Singular Integrals Numerically