Weighted Fejér constants and Fekete sets

Abstract

We give the connections among the Fekete sets, the zeros of orthogonal polynomials, 1(w)-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fejér contants. Finally the convergence of a weighted Grünwald interpolation is proved.

The electrostatic properties of zeros of exceptional Laguerre and Jacobi polynomials and stable interpolation

“…To this purpose we adapt some methods to exceptional orthogonal polynomials, which were developed to the general ones. Since the regular zeros of exceptional polynomials form a minimal energy (or Fekete) system under a suitable external field, similarly to [14] we will show that on these sets one can build up stable interpolation operators which are the most economical as well. Finally the notion of Fekete sets and nth transfinite diameter allows to investigate the behavior of the energy function when the number of the points tends to infinity.…”

“…(1) As it was pointed out in [14], the assumption: − (log v) ′′ > 0 on (0, ∞) ensures the uniqueness of the system of minimal energy. In Lemma 1 we have seen that this is exactly the opposite of the first term in H i,i that is…”

“…[15,14]). Our main tool is the differential equation of orthogonal polynomials, and its transformed version to a Schrödinger equation (cf.…”

“…The generalization of the results of [17] to any classical weights can be found in [24]. For results on general weights, and on Fekete sets as optimal sets of interpolation, see [14].…”

p-Transfinite diameter and p-Chebyshev constant in locally compact spaces

“…e.g. [21], [15]). The aim of the investigations below is to get something similar in the nonlinear case.…”