Browsing by Author "Eichinger, Benjamin"
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Item Orthogonal rational functions with real poles, root asymptotics, and GMP matrices(American Mathematical Society, 2023) Eichinger, Benjamin; Lukić, Milivoje; Young, GiorgioThere is a vast theory of the asymptotic behavior of orthogonal polynomials with respect to a measure on and its applications to Jacobi matrices. That theory has an obvious affine invariance and a very special role for . We extend aspects of this theory in the setting of rational functions with poles on, obtaining a formulation which allows multiple poles and proving an invariance with respect to preserving Möbius transformations. We obtain a characterization of Stahl–Totik regularity of a GMP matrix in terms of its matrix elements; as an application, we give a proof of a conjecture of Simon – a Cesàro–Nevai property of regular Jacobi matrices on finite gap sets.