Rendiconti Lincei - Matematica e Applicazioni


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Volume 19, Issue 1, 2008, pp. 1–23
DOI: 10.4171/RLM/505

Published online: 2008-03-31

Spectral analysis of transfer operators associated to Farey fractions

Claudio Bonanno[1], Sandro Graffi[2] and Stefano Isola[3]

(1) Università di Pisa, Italy
(2) Università di Bologna, Italy
(3) Università di Camerino, Italy

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.

Keywords: Transfer operators, Farey fractions, spectral theory, period functions, self-reciprocal functions

Bonanno Claudio, Graffi Sandro, Isola Stefano: Spectral analysis of transfer operators associated to Farey fractions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), 1-23. doi: 10.4171/RLM/505