Classification of singular integrals over a local field

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...

Numerical quadrature for high-dimensional singular integrals over parallelotopes

We introduce and analyze a family of algorithms for an efficient numerical approximation of integrals of the form I = ∫ C(1) ∫ C(2) F (x, y, y−x)dydx where C, C are d-dimensional parallelotopes (i.e. affine images of d-hypercubes) and F has a singularity at y − x = 0. Such integrals appear in Galerkin discretization of integral operators in R. We construct a family of quadrature rules QN with N...

A General New Algorithm for Regulaization of Singular Integrals in Three-Dimensional Boundary Elemnts

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

Multi-parameter singular integrals

Evaluating Singular and Nearly Singular Integrals Numerically