On the minium problem of the kernel function

Abstract

Let D be any bounded simply-connected domain in the z-plane. The purpose of this thesis is to study some properties of the kernel function in D. and we determine functions f(z) which satisfy f(t) = 1 at a fixed point t of a domain D and which minimize the integral (f, f). Finally, we define the Green's function and find the relationship between the kernel function and the Green's function.