%0 Unpublished work
%T Salem-Schaeffer measures of dynamical system origin
%+ Institut de Mathématiques de Marseille (I2M)
%A Prikhodko, Alexander
%Z A*Midex
%8 2014-04-27
%D 2014
%K Rajchman measure
%K Salem measure
%K ergodic theory
%K spetral invariants
%K mixing
%Z Mathematics [math]/Classical Analysis and ODEs [math.CA]
%Z Mathematics [math]/Dynamical Systems [math.DS]Preprints, Working Papers, ...
%X A class of measure preserving actions of the groups $Z^d$ and $R^d$ is constructed possessing the following properties: the spectrum of the action is simple and for a dense set of functions $f$ the spectral measures $\sigma_f$ have an extremal rate of the Fourier coefficient decay: $\hat\sigma_f(n) = O(|n|^{-d/2+\varepsilon})$ for any $\varepsilon > 0$, where the exponent $-d/2$ is the minimal possible for singular mesures on the torus $T^d$.
%G English
%Z Théorie ergodique dans ses applications aux processus stochastiques
%Z théorie des représentations et théorie de Teichmüller
%2 https://hal.science/hal-00984141/document
%2 https://hal.science/hal-00984141/file/NoteOnIcebergActionsE.pdf
%L hal-00984141
%U https://hal.science/hal-00984141
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS
%~ AMIDEX
%~ ANR