arXiv subjects
Publications and source records attributed to L. G. González Ricardo.
We obtain the strong asymptotics of multiple orthogonal polynomials which arise in a mixed type Hermite-Padé approximation problem defined on a Nikishin system of functions. The results obtained allow to give exact estimates of the rate of convergence of the approximating rational functions and the strong asymptotics of Cauchy biorthogonal polynomials.
We give the strong asymptotic of Cauchy biorthogonal polynomials under the assumption that the defining measures are supported on non intersecting intervals of the real line and satisfy Szegő's condition. The biorthogonal polynomials are connected with certain mixed type Hermite-Padé polynomials, which verify full orthogonality relations with respect to some varying measures. Thus, the strong asymptotic of orthogonal polynomials with respect to varying measures plays a key role in the study.
In the present paper we prove a Stieltjes type theorem on the convergence of a sequence of rational functions associated with a mixed type Hermite-Padé approximation problem of a Nikishin system of functions and analyze the ratio asymptotic of the corresponding Hermite-Padé polynomials.
We study the logarihtnmic asymptotic of multiple orthogonal polynomials arising in a mixed type Hermite-Padé approximation problem associated with the rational perturbation of a Nikishin system of functions. The formulas obtained allow to give exact estimates of the rate of convergence of the corresponding Hermite-Padé approximants.
The present paper deals with the convergence properties of multi-level Hermite-Padé approximants for a class of meromorphic functions given by rational perturbations with real coefficients of a Nikishin system of functions, and study the zero location of the corresponding multiple orthogonal polynomials.