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Strong Asymptotics of Hermite-Padé Approximants for Angelesco Systems

  Published:2016-01-22
 Printed: Oct 2016
  • Maxim L. Yattselev,
    Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 North Blackford Street, Indianapolis, IN 46202
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Abstract

In this work type II Hermite-Padé approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.
Keywords: Hermite-Padé approximation, multiple orthogonal polynomials, non-Hermitian orthogonality, strong asymptotics, matrix Riemann-Hilbert approach Hermite-Padé approximation, multiple orthogonal polynomials, non-Hermitian orthogonality, strong asymptotics, matrix Riemann-Hilbert approach
MSC Classifications: 42C05, 41A20, 41A21 show english descriptions Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]
Approximation by rational functions
Pade approximation
42C05 - Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]
41A20 - Approximation by rational functions
41A21 - Pade approximation
 

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