Asymptotic inversion of Toeplitz matrices with one singularity in the symbol
Philippe Rambour, Abdellatif Seghier · Comptes Rendus Mathématique · 2009
We consider the function f α defined by f α ( θ ) = | 1 − e i θ | 2 α f 1 ( e i θ ) with f 1 a regular strictly positive function and α a real number with − 1 2 0 . We obtain also an asymptotic expansion of the coefficients of the orthogonal polynomials associated to the function f α and we give an answer to a question of H. Kesten (1961).