Ratio asymptotics of Hermite-Padé polynomials for Nikishin systems

A I Aptekarev, Guillermo L López, I A Rocha
2005 Sbornik. Mathematics  
We prove the existence of ratio asymptotic for a sequence of multiple orthogonal polynomials which share orthogonality relations with a collection of m finite Borel measures supported on a bounded interval of the real line and constitute a so called Nikishin system of measures. When m = 1 our result reduces to E. A. Rakhmanov's known Theorem on ratio asymptotic for orthogonal polynomials on a segment.
doi:10.1070/sm2005v196n08abeh002329 fatcat:oavf5pdxejaxjmkfato2bfdkv4