Spectral analysis of transfer operators associated to Farey fractions
Mathematical Physics
2007-08-07 v1 Dynamical Systems
math.MP
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.
Keywords
Cite
@article{arxiv.0708.0686,
title = {Spectral analysis of transfer operators associated to Farey fractions},
author = {Claudio Bonanno and Sandro Graffi and Stefano Isola},
journal= {arXiv preprint arXiv:0708.0686},
year = {2007}
}
Comments
28 pages, 1 figure