1. C. H. FitzGerald considered
conditions for interpolating the values of an analytic function in terms of
quadratic inequalities. In addition, he used them to obtain an interesting result
concerning analytic continuation of functions of two variables and related them to
Pick-Nevanlinna interpolation.
We shall show that these theorems follow directly from well-known principles of
functional analysis. Since these principles are not limited to interpolating values of an
analytic function, we shall obtain applications to interpolating functional values of
both analytic and harmonic functions of several variables. In addition, we obtain
analogous applications to analytic and harmonic continuation and to Pick-Nevanlinna
interpolation.
