Absolute continuity and singularity of spectra for the flows $T_t\otimes T_{at}$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 88-92
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Given disjoint countable dense subsets $C$ and $D$ of the half-line $(1,+\infty)$, there exists a flow $T_t$ preserving a sigma-finite measure and such that all automorphisms $T_1\otimes T_{c}$ with $c\in C$ have simple singular spectrum and all automorphisms $T_1\otimes T_{d}$ with $d\in D$ have Lebesgue spectrum of countable multiplicity.
Keywords:
tensor product of flows, absolutely continuous singular spectrum, dissipativity, weak limits of operators.
@article{FAA_2022_56_3_a5,
author = {V. V. Ryzhikov},
title = {Absolute continuity and singularity of spectra for the flows $T_t\otimes T_{at}$},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {88--92},
year = {2022},
volume = {56},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a5/}
}
V. V. Ryzhikov. Absolute continuity and singularity of spectra for the flows $T_t\otimes T_{at}$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 88-92. http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a5/