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arXiv · 0708.0686

Spectral analysis of transfer operators associated to Farey fractions

Claudio Bonanno·Sandro Graffi·Stefano Isola
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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.

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Claudio Bonanno, Sandro Graffi, Stefano Isola. 2007-08-05. Spectral analysis of transfer operators associated to Farey fractions. https://arxiv.org/abs/0708.0686

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