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arXiv · 1205.6964

Singular Schaeffer-Salem measures of dynamical system origin

A. A. Prikhod'ko
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Abstract

We study a class of dynamical systems given by measure preserving actions of the group $Z^d$ or $R^d$ and generating a set of spectral measures with an extremal rate of the Fourier coefficient decay: $\Hat\sigma(n) = O(|n|^{-1/2+\epsilon})$ for any $\epsilon > 0$. Singular measures with this property are investigated in works due to Wiener and Wintner, Schaeffer, Salem, Ivashev-Musatov, Zygmund et al. Thus, the discovered effect provides a new construction of singular distributions of Schaeffer-Salem type on the torus $T^d$ and in the space $R^d$.

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BibTeXRIS

A. A. Prikhod'ko. 2012-05-31. Singular Schaeffer-Salem measures of dynamical system origin. https://arxiv.org/abs/1205.6964

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