Determinants of harmonic matrices

Abstract

This paper is concerned with extensions of a theorem by H. S. Wall (Theorem 3 of [3 ]): if M is a 2 X 2 harmonic matrix and F corresponds to M then det M= 1 only in case Fll = F22. As in [3] let H. denote the class of nXn harmonic matrices and n the class of n Xn matrices F of complex-valued functions from the real numbers, continuous and of bounded variation on every interval, such that F(O) = 0. In [3] Wall has shown that the Stieltjes integral equation,