Special weak limits and simple spectrum of the
Sbornik. Mathematics, Tome 209 (2018) no. 5, pp. 660-671
Voir la notice de l'article provenant de la source Math-Net.Ru
An example of a measure-preserving flow $T_t$ for which the tensor product
$T_t\otimes T_{\alpha t}$ has simple spectrum for all $\alpha > 1$ is
constructed. The construction of the flow uses asymptotically infinitesimal
spacers and spacers obtained using results in finite field theory. For the
spectral measure $\sigma$ of a flow of this type, any nonorthogonal
projection of the measure $\sigma\times\sigma$ onto the diagonal in $\mathbb
R\times \mathbb R$ is a 1-1 mapping $(\operatorname{mod} 0)$ with respect to
the measure $\sigma\times\sigma$.
Bibliography: 12 titles.
Keywords:
ergodic flow, lacunar rigidity, Galois fields, special weak limits,
simple spectrum, tensor product.
@article{SM_2018_209_5_a2,
author = {M. S. Lobanov and V. V. Ryzhikov},
title = {Special weak limits and simple spectrum of the},
journal = {Sbornik. Mathematics},
pages = {660--671},
publisher = {mathdoc},
volume = {209},
number = {5},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2018_209_5_a2/}
}
M. S. Lobanov; V. V. Ryzhikov. Special weak limits and simple spectrum of the. Sbornik. Mathematics, Tome 209 (2018) no. 5, pp. 660-671. http://geodesic.mathdoc.fr/item/SM_2018_209_5_a2/