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.