JournalsrlmVol. 19 , No. 1DOI 10.4171/rlm/505

Spectral analysis of transfer operators associated to Farey fractions

  • Sandro Graffi

    Università di Bologna, Italy
  • Claudio Bonanno

    Università di Pisa, Italy
  • Stefano Isola

    Università di Camerino, Italy
Spectral analysis of transfer operators associated to Farey fractions cover

Abstract

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.