368 research outputs found
Asymptotics of polynomials orthogonal over circular multiply connected domains
Let be a domain obtained by removing, out of the unit disk ,
finitely many mutually disjoint closed disks, and for each integer ,
let be the monic th-degree polynomial satisfying the
planar orthogonality condition , . Under a certain assumption on the domain , we establish asymptotic
expansions and formulae that describe the behavior of as
at every point of the complex plane. We also give an asymptotic expansion
for the squared norm
Strong Asymptotics of Hermite-Pad\'e Approximants for Angelesco Systems
In this work type II Hermite-Pad\'e 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.Comment: 40 page
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