Asymptotic of the terms of the Gegenbauer polynomial on the unit circle and applications to the inverse of Toeplitz matrices

2013/10/17 by Philippe Rambour, Rambour, Philippe · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1310.4685

arxiv created 2014/06/13 · arxiv updated 2014/06/16

Abstract

The first part of this paper is devoted to the study of the orthogonal polynomial on the circle, with respect of a weight of type f_α(θ) = (2cos θ- 2cos θ₀)^2α c₁ with θ₀ ∈ ]0,π[, -1/2 <α<1/2 and c₁ a sufficiently smooth function. In a second part of the paper we obtain an asymptotic of the entries (T_N f_α)^-1_k+1,l+1 for sufficiently large values of k,l, that provides a lower bound on the eigenvalues of this matrix.

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