Determining the first radii of meromorphy via orthogonal polynomials on the unit circle

Abstract

Applying a result concerning a convergence of modified orthogonal Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard’s theorem for determining the radius of 1-meromorphy of a function holomorphic on the closed unit disk. Furthermore, we apply our result to study analytic properties of the reciprocal of Szegő functions when their corresponding sequence of Verblunsky coefficients has exponential decay.