Related papers: Hermite-Pad\'e approximation for certain systems o…
We study the convergence of type I Hermite-Pad\'e approximation for a class of meromorphic functions obtained by adding a vector of rational functions with real coefficients to a Nikishin system of functions.
The present paper deals with the convergence properties of multi-level Hermite-Pad\'e approximants for a class of meromorphic functions given by rational perturbations with real coefficients of a Nikishin system of functions, and study the…
Pad\'e approximation has two natural extensions to vector rational approximation through the so called type I and type II Hermite-Pad\'e approximants. The convergence properties of type II Hermite-Pad\'e approximants have been studied. For…
Hermite-Pad\'e approximants of type II are vectors of rational functions with common denominator that interpolate a given vector of power series at infinity with maximal order. We are interested in the situation when the approximated vector…
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-Pad\'e approximation problem of a Nikishin system of functions and analyze the ratio…
In this work we present new results on the convergence of diagonal sequences of certain mixed type Hermite-Pad\'e approximants of a Nikishin system. The study is motivated by a mixed Hermite-Pad\'e approximation scheme used in the…
A survey of direct and inverse type results for row sequences of Pad\'e and Hermite-Pad\'e approximation is given. A conjecture is posed on an inverse type result for type II Hermite-Pad\'e approximation when it is known that the sequence…
We study the logarihtnmic asymptotic of multiple orthogonal polynomials arising in a mixed type Hermite-Pad\'e approximation problem associated with the rational perturbation of a Nikishin system of functions. The formulas obtained allow to…
We obtain the strong asymptotics of multiple orthogonal polynomials which arise in a mixed type Hermite-Pad\'e approximation problem defined on a Nikishin system of functions. The results obtained allow to give exact estimates of the rate…
We show that solution to the Hermite-Pad\'{e} type I approximation problem leads in a natural way to a subclass of solutions of the Hirota (discrete Kadomtsev-Petviashvili) system and of its adjoint linear problem. Our result explains the…
We obtain extensions of the Poincar\'e and Perron theorems for higher order recurrence relations and apply them to obtain an inverse type theorem for row sequences of (type II) Hermite-Pad\'e approximation of a vector of formal power…
The main purpose of this paper is to compare the convergence properties of Pad\'e approximants and rational Hermite-Pad\'e approximants for some model class of multivalued analytic functions based of the inverse Zhoukovsky transform. We…
We give a Montessus de Ballore type theorem for row sequences of Hermite-Pad\'e approximations of vector valued analytic functions refining some results in this direction due to P.R. Graves-Morris and E.B. Saff. We do this introducing the…
In this paper we study linear and non-linear Fourier-Pad\'e approximation for Angelesco systems of functions. This construction is similar to that of Hermite-Pad\'e approximation. Instead of considering power series expansions of the…
Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of…
Given a system of functions $\textup{\textbf{F}}=(F_1,\ldots,F_d),$ analytic on a neighborhood of some compact subset $E$ of the complex plane with simply connected complement, we define a sequence of vector rational functions with common…
In this paper, we estimate the simultaneous approximation exponents of the values of certain Mahler functions. For this we construct Hermite-Pad\'{e} approximations of the functions under consideration, then apply the functional equations…
We develop an underlying relationship between the theory of rational approximations and that of isomonodromic deformations. We show that a certain duality in Hermite's two approximation problems for functions leads to the Schlesinger…
We give a short introduction to Pade approximation (rational approximation to a function with close contact at one point) and to Hermite-Pade approximation (simultaneous rational approximation to several functions with close contact at one…
The aim of this paper is to investigate the quality of approximation of almost time and band limited functions by its expansion in the Hermite and scaled Hermite basis. As a corollary, this allows us to obtain the rate of convergence of the…