Correction to: Quantitative Approximation by Nonlinear Picard–Choquet, Gauss–Weierstrass–Choquet and Poisson–Cauchy–Choquet Singular Integrals

Quantitative Uniform Approximation by Generalized Discrete Singular Operators

Here we study the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular operators. We treat both the unitary and non-unitary cases of the operators above. We establish quantitatively the pointwise and uniform convergences of these operators to the unit operator by involving the uniform higher modulus of smoothness of a uni...

Applications and Lipschitz results of Approximation by Smooth Picard and Gauss-Weierstrass Type Singular Integrals

We continue our studies in higher order uniform convergence with rates and in Lp convergence with rates. Namely, in this article we establish some Lipschitz type results for the smooth Picard type singular integral operators and for the smooth GaussWeierstrass type singular integral operators. RESUMEN Continuamos nuestros estudios sobre convergencia uniforme de orden superior con radios y sobre...

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...

Evaluating Singular and Nearly Singular Integrals Numerically

Multi-parameter singular integrals