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arXiv · 1806.10884

Riesz products and spectral decompositions for rank 1 measure preserving transformations

Yury A. Neretin
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Abstract

We consider rank one measure preserving transformations $g$ and the corresponding Koopman unitary operators $U(g)$. It is known that a generic (in the sense of Baire category) measure preserving transformation has rank one, spectral measure of $U(g)$ is purely singular and is given by a Riesz product. For such transformations we write explicitly spectral decompositions of operators $U(g)$ in generalized eigenfunctions.

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Yury A. Neretin. 2018-06-28. Riesz products and spectral decompositions for rank 1 measure preserving transformations. https://arxiv.org/abs/1806.10884

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