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

Bosuwan N.Mahidol University2024-03-132024-03-132024-01-01Dolomites Research Notes on Approximation Vol.17 No.1 (2024) , 12-21https://repository.li.mahidol.ac.th/handle/20.500.14594/97557Applying 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.MathematicsDetermining the first radii of meromorphy via orthogonal polynomials on the unit circleArticleSCOPUS10.14658/PUPJ-DRNA-2024-1-22-s2.0-8518647141520356803