Valeur propre minimale d'une matrice de Toeplitz et d'un produit de matrices de Toeplitz.

This paper is essentially devoted to the study of the minimal eigenvalue $\lambda_{N,\alpha}$ of the Toepllitz matrice $T_N(\varphi_{\alpha})$ where $\varphi_{\alpha}(e^{i \theta})=\vert 1- e^{i \theta} \vert ^{2\alpha} c_{1}(e^{i \theta})$ with $c_{1}$ a positive sufficiently smooth function and $0<\alpha \frac{1}{2}$ we obtain the asymptotic of the minimal eigenvalue of $T_N (\varphi {\alpha_1}) T_N (\varphi {\alpha_2}).$