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arXiv math/04082592004-08-19math.SPmath-phmath.MP

非对易Perron-Frobenius-Ruelle定理，双权希尔伯特变换和概周期性

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

A. Volberg, P. Yuditskii

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摘要：

研究了双曲多项式映射的平衡测度生成的Jacobi矩阵。Bellissard的猜想说，这个矩阵应该具有极强的周期性。我们展示了这个猜想是如何与一定的非交换版本的Bowen-Ruelle理论，以及如何两个重量希尔伯特变换自然出现在这种情况下。

英文摘要：

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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