Théorèmes de trace de type Szegö dans le cas singulier

Let f be a function eiθ→f(eiθ)=|1−eiθ|2αf1(eiθ) with f1 a regular strictly positive function and a real number α in ]−1/2,1/2[∖{0}. In a previous paper for such a number α we have obtained the asymptotic behaviour of the entries of the inverse of the Toeplitz matrix TN,f when N goes to infinity. These results allow us to give trace formulas, which extend a classical expression of Szegö's limits theorems.