We study the so-called Fekete points which maximize Vandermonde determinants of the form V_a(x_1,...,x_n)=det(x_i^{a_j}), i,j=1..N where the x_i are distincts points belonging to the interval [a,b] of the real line and a_j's are ordered integers. We prove that every Vandermonde determinant, so generalized, can be factored as a product of the corresponding classical Vandermonde determinant and a homogeneous symmetric function of the points, a {\it Schur function}, and that the resulting generalized Fekete points have the same asymptotic distribution as the classical ones.
Fekete points for bivariate polynomials restricted to y=x^m
DE MARCHI, STEFANO
2000
Abstract
We study the so-called Fekete points which maximize Vandermonde determinants of the form V_a(x_1,...,x_n)=det(x_i^{a_j}), i,j=1..N where the x_i are distincts points belonging to the interval [a,b] of the real line and a_j's are ordered integers. We prove that every Vandermonde determinant, so generalized, can be factored as a product of the corresponding classical Vandermonde determinant and a homogeneous symmetric function of the points, a {\it Schur function}, and that the resulting generalized Fekete points have the same asymptotic distribution as the classical ones.File in questo prodotto:
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