Sebastien Gouezel
spectre de l'op{\'e}rateur de transfert en dimension 1
(500K, Postscript)

ABSTRACT.  We study the spectral properties of a transfer operator 
$\mathcal{M}\Phi(x)=\sum_{\omega}g_{\omega}(x)\Phi(\psi_\omega x)$ 
acting on functions of bounded variation. After estimations 
- using a symetrical integral - of the spectral radius and 
of the essential spectral radius, we consider the dynamical 
determinant $\Det^\#(\Id+z\boM)$. We generalize to the case of 
discontinuous weights the results of Baladi and Ruelle (for 
continuous weights) on the link between zeros of the sharp determinant 
and eigenvalues of the transfer operator. The proof, by regularization 
of the weights, uses a spectral result giving the surjectivity of 
some applications between eigenspaces of operators.