Orthogonal polynomials with respect of a class of Fisher-Hartwig symbols

2014/06/06 by Rambour, Philippe
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.1806

Abstract

In this paper we give an asymptotic of the coefficients of the orthogonal polynomials on the unit circle, with respect of a weight of type f : θ↦ ∏_{1≤ j ≤ M} \vert 1 - e^i(θ_j-θ)\vert ^2α_j c with θ_j∈ ]-π,π], -(1)/(2) < α_j

Related

• Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
• Asymptotic of the terms of the Gegenbauer polynomial on the unit circle and applications to the inverse of Toeplitz matrices
• Orthogonal polynomials on the circle for the weight w satisfying conditions: w,1/w in BMO(T)
• The growth of polynomials orthogonal on the unit circle with respect to a weight w that satisfies w,1/w ∈ L^∞(\mathbbT)
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