Dirichlet integral dual-access collocation-kernel space analytic interpolation for unit disks: DIDACKS I

Abstract

This article presents a technique for analytic interpolation over the exterior of a unit disk using complex poles in the interior--as well as corresponding techniques for the exterior of a real unit disk and for the interior of a real and complex unit disk. This is accomplished by developing special kernel spaces labeled dual-access collocation-kernel spaces. Higher order pole and logarithmic point source kernels are also considered. Relationships to Szego and Bergman kernel theory are addressed.