Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in extC(z). The overlapping space $varepsilon$(W) of D(W) in C(z) is a Herglotz space with Herglotz function $varphi$(z) which satisfies $varphi$(z) + ${varphi}^*(z^{-1})$ = 2[1-W$^*(z^{-1})W(z)]$.