Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicity
Spectral Theory
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We consider the Jacobi matrix generated by a balanced measure of hyperbolic polynomial map. The conjecture of Bellissard says that this matrix should have an extremely strong periodicity property. We show how this conjecture is related to a certain noncommutative version of Bowen--Ruelle theory, and how the two weight Hilbert transform naturally appears in this context.
Keywords
Cite
@article{arxiv.math/0408259,
title = {Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicity},
author = {A. Volberg and P. Yuditskii},
journal= {arXiv preprint arXiv:math/0408259},
year = {2007}
}