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We improve the class of indices for which normality takes place in a Nikishin system and apply this in Hermite-Padé approximation of such systems of functions.

We consider the solutions of general three term recurrence relations whose coefficients are analytic functions in a prescribed region. We study the ratio asymptotic of such solutions under the assumption that the coefficients are asymptotically periodic and their strong asymptotic under more restrictive conditions.

Let be a finite positive Borel measure with compact support consisting of an interval [c, d] ⊂ R plus a set of isolated points in R\[c, d], such that > 0 almost everywhere on [c, d]. Let {w 2n }, n ∈ Z + , be a sequence of polynomials, deg w 2n 2n, with real coefficients whose zeros lie outside the smallest interval containing the support of. We prove ratio… (More)

We study the zero location and asymptotic zero distribution of sequences of polynomials which satisfy an extremal condition with respect to a norm given on the space of all polynomials.

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and… (More)

K. Mahler introduced the concept of perfect systems in the theory of simultaneous Hermite-Padé approximation of analytic functions. Recently, we proved that Nikishin systems, generated by measures with bounded support and non-intersecting consecutive supports contained on the real line, are perfect. Here, we prove that they are also perfect when the… (More)

In this paper we investigate general properties of the coefficients in the recurrence relation satisfied by multiple orthogonal polynomials. The results include as particular cases Angelesco and Nikishin systems.

For a wide class of Sobolev type norms with respect to measures with unbounded support on the real line, the contracted zero distribution and the logarithmic asymptotic of the corresponding re-scaled Sobolev orthogonal polynomials is given.

Using a convergence theorem for Fourier-Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk.