  This article addresses the interpolation of harmonic functions over the
interior of a $\mathbb{R}^3$ unit sphere by linear combinations of
fundamental-solution point-source basis functions, where all the sources are
assumed to be outside the sphere. Since the source and field points are in
different domains, the fundamental-solution basis functions are bounded and can
be regarded as defining a new type of kernel space that is related to
reproducing kernel Hilbert space (RKHS), but is different from it and which is
labeled a Dirichlet integral dual-access collocation-kernel space (DIDACKS).
DIDACKS theory has direct implications for the method of fundamental solutions
(MFS) and some for the fast multipole method (FMM) and boundary element method
(BEM).
