Seminari del Dipartimento di Matematica

Seminario del 2014

Claudio Bonanno (Università di Pisa)

The eigenfunctions of the transfer operator of the Farey map and their role in the spectral theory on the modular surface

fisica matematica

In this talk I first discuss the existence of eigenfunctions for the transfer operator of the Farey map. The main problem is that these operators are not quasi-compact on spaces of C^k functions for any k. However, on a suitable space of holomorphic functions, it is possible to have a characterization of the eigenfunctions. Then in the second part I will show that these eigenfunctions are related to Maass cusp and non-cusp forms of the modular surface, that is eigenfunctions of the hyperbolic Laplacian on the hyperbolic half-plane quotiented by the action of full modular group PSL(2,Z). This is joint work with Stefano Isola.