Eisenstein integrals and singular Cauchy problems

Numerical Evaluation of Cauchy Principal Value Integrals with Singular Integrands

Convergence results are proved for sequences of interpolatory integration rules for Cauchy principal value integrals of the form -l k(x)(f(x)/(x-X))dx, -1<A<1, -i when f(x) is singular at a point { / À and the singularity is ignored or avoided. /:'

Singular Integrals and Elliptic Boundary Problems on Rough Domains

These notes discuss results on layer potential methods for elliptic boundary problems, with emphasis on the Dirichlet problem for the Laplace operator. They start by reviewing results for domains with moderately smooth boundary, then for Lipschitz domains, and proceed to discuss results in [HMT], obtained with S. Hofmann and M. Mitrea, for a class of domains we call regular Semmes-KenigToro (SK...

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

Some remarks about Cauchy integrals

A basic theme in the wonderful books and surveys of Stein, Weiss, and Zygmund is that Hilbert transforms, Poisson kernels, heat kernels, and related objects are quite interesting and fundamental. I certainly like this point of view. There is a variety of ways in which things can be interesting or fundamental, of course. In the last several years there have been striking developments connected t...