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On Multipoint Padé Approximants whose Poles Accumulate on Contours that Separate the Plane

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Abstract

In this note, we consider asymptotics of the multipoint Padé approximants to Cauchy integrals of analytic nonvanishing densities defined on a Jordan arc connecting \( -1 \) and \( 1 \). We allow for the situation where the (symmetric) contour attracting the poles of the approximants separates the plane.

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Notes

  1. This definition yields one additional interpolation condition at infinity.

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Funding

This work was supported in part by a grant from the Simons Foundation, CGM-706591, and by Moscow Center for Fundamental and Applied Mathematics, Agreement with the Ministry of Science and Higher Education of the Russian Federation, No. 075-15-2019-1623.

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Authors and Affiliations

  1. Indiana University-Purdue University Indianapolis, Indianapolis, Indiana, 46202, USA

    M. L. Yattselev

  2. Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia

    M. L. Yattselev

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  1. M. L. Yattselev
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Correspondence to M. L. Yattselev.

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Yattselev, M.L. On Multipoint Padé Approximants whose Poles Accumulate on Contours that Separate the Plane. Math Notes 110, 784–795 (2021). https://doi.org/10.1134/S0001434621110158

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  • DOI: https://doi.org/10.1134/S0001434621110158

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