Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicity

Details Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicity Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicity

2004-08-19

arxiv.org/abs/math/0408259v1

Mathematics

Spectral Theory

Scientific paper

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.

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