The spectrum of a one-parameter family of signed transfer operators associated to the Farey map is studied in detail. We show that when acting on a suitable Hilbert space of analytic functions they are self-adjoint and exhibit absolutely continuous spectrum and no non-zero point spectrum. Polynomial eigenfunctions when the parameter is a negative half-integer are also discussed.
Cite this article
Sandro Graffi, Claudio Bonanno, Stefano Isola, Spectral analysis of transfer operators associated to Farey fractions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 1, pp. 1–23DOI 10.4171/RLM/505