Spectral analysis of transfer operators associated to Farey fractions

Details Spectral analysis of transfer operators associated to Farey fractions Spectral analysis of transfer operators associated to Farey fractions

2007-08-05

arxiv.org/abs/0708.0686v1

Physics

Mathematical Physics

28 pages, 1 figure

Scientific paper

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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