Une extension d'un résultat de Szegö sur les valeurs propres des matrices de Toeplitz

Abstract: In this paper we consider a class of non-negative, 2π-periodic, even functions. For such a function f we obtain an asymptotic of the eigenvalues of the Toeplitz matrice such goes to a positive real when N goes to the infinity. for all real , we infer from this result the asymptotic of the same eigenvalues of the Toeplitz matrice , where , and a regular function. With these hypotheses we give also the order of the little nad of the greatest eigenvalue of the matrix. [Copyright &y& Elsevier]