Spectral analysis of transfer operators associated to Farey fractions

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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.
28 pages, 1 figure

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Mathematical Physics, Dynamical Systems, 58F20, 58F25, 11F72, 11M26

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http://salesiana.dossiersoluciones.com/handle/123456789/135599

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.0686
 http://arxiv.org/abs/0708.0686

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arXiv