Asymptotic of Cauchy biorthogonal polynomials

2019/03/30 by U. Fidalgo, Fidalgo, U., G. López Lagomasino +4 · 1 citation
Mathematics · #Approximation Theory and Sequence Spaces #Mathematical Approximation and Integration #Mathematical functions and polynomials #math.CA #msc:30E10 #msc:41A21 #msc:42C05

paper · pdf · doi:10.48550/arxiv.1904.00126

27 pages

arxiv created 2019/03/30 · arxiv updated 2019/04/02

Abstract

We consider sequences of biorthogonal polynomials with respect to a Cauchy type convolution kernel and give the weak and ratio asymptotic of the corresponding sequences of biorthogonal polynomials. The construction is intimately related with a mixed type Hermite-Padé approximation problem whose asymptotic properties is also revealed.

Cited by

• Logarithmic asymptotic of multi-level Hermite-Padé polynomials

Related

• Cauchy Biorthogonal Polynomials
• Strong asymptotic of Cauchy biorthogonal polynomials and orthogonal polynomials with varying measure
• Strong asymptotics of multi-level Hermite-Padé polynomials
• Asymptotic properties of biorthogonal polynomials systems related to Hermite and Laguerre polynomials
• Ratio asymptotic for bi-orthogonal matrix polynomials with unbounded recurrence coefficients