Weighted approximation by double singular integral operators with radially defined kernels

Statistical Approximation by Double Picard Singular Integral Operators

We first construct a sequence of double smooth Picard singular integral operators which do not have to be positive in general. After giving some useful estimates, we mainly show that it is possible to approximate a function by these operators in statistical sense even though they do not obey the positivity condition of the statistical Korovkin theory.

Convolution Calderón-Zygmund singular integral operators with rough kernels

A survey of known results in the theory of convolution type Calderón-Zygmund singular integral operators with rough kernels is given. Some recent progress is discussed. A list of remaining open questions is presented.

High-Order Quadratures for Integral Operators with Singular Kernels

A numerical integration method that has rapid convergence for integrands with known singularities is presented. Based on endpoint corrections to the trapezoidal rule, the quadratures are suited for the discretization of a variety of integral equations encountered in mathematical physics. The quadratures are based on a technique introduced by Rokhlin (Computers Math. Applic. 20, pp. 51-62, 1990)...

Weighted norm inequalities for singular integral operators

On approximation properties of sampling operators defined by dilated kernels

In this paper we consider some generalized Shannon sampling operators, which are defined by band-limited kernels. In particular, we use dilated versions of some previously known kernels. We give also some examples of using sampling operators with dilated kernels in imaging applications.