The Singular Value Decomposition of the Poisson Kernel

Abstract

The Poisson kernel is the solution operator for the Dirichlet problem for Laplace’s equation. As such, on bounded regions $\Omega \subseteq {ℝ}^N$ with mild regularity, it is a compact linear transformation of $L^2\left(\partial \Omega \right)$ to $L^2\left(\Omega \right)$. This talk will outline the singular value decomposition of this operator. The analysis also enables a bound on a constant in an inequality of Hassell and Tao.