Strong asymptotics of extremal polynomials on the segment in the presence of denumerable set of mass points

Rabah Khaldi; Ahcene Boucenna

doi:10.33993/jnaat401-949

Authors

Rabah Khaldi University of Annaba, Algeria
Ahcene Boucenna University of Annaba, Algeria

DOI:

https://doi.org/10.33993/jnaat401-949

Keywords:

orthogonal polynomials, asymptotic behavior

Abstract views: 227

Abstract

The strong asymptotics of the monic extremal polynomials with respect to a \(L_{p}(\sigma )\) norm are studied. The measure \(\sigma \) is concentrated on the segment \([-1,1]\) plus a denumerable set of mass points which accumulate at the boundary points of \([-1,1]\) only. Under the assumptions that the mass points satisfy Blaschke's condition and that the absolutely continuous part of \(\sigma \) satisfies Szeg?'s condition.

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