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Let _ be a finite positive Borel measure supported on an arc # of the unit circle, such that _$>0 a.e. on #. We obtain a theorem about the weak convergence of the corresponding sequence of orthonormal polynomials. Moreover, we prove an analogue of the Szego Geronimus theorem on strong asymptotics of the orthogonal polynomials on the complement of #, which… (More)
We obtain a result on convergence of Padé approximants for meromorphic functions of Stieltjes type. Connection of Padé approximants with Stieltjes moment problem plays a key role in the proof.
We study some properties of the zeros and the asymptotic behavior of orthogonal polynomials with respect to varying measures on the unit circle. In the proofs, some techniques of rational approximation are used.