Geodesic
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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a5/}
}
TY  - JOUR
AU  - V. V. Ryzhikov
TI  - Absolute continuity and singularity of spectra for the flows $T_t\otimes T_{at}$
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2022
SP  - 88
EP  - 92
VL  - 56
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a5/
LA  - ru
ID  - FAA_2022_56_3_a5
ER  - 
%0 Journal Article
%A V. V. Ryzhikov
%T Absolute continuity and singularity of spectra for the flows $T_t\otimes T_{at}$
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2022
%P 88-92
%V 56
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a5/
%G ru
%F 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/

[1] Z. I. Bezhaeva, V. I. Oseledets, Zap. nauchn. sem. POMI, 326, 2005, 28–47 | Zbl

[2] Z. I. Bezhaeva, V. I. Oseledets, Funkts. analiz i ego pril., 44:2 (2010), 3–13 | DOI | MR | Zbl

[3] V. V. Ryzhikov, Matem. zametki, 106:6 (2019), 894–903 | DOI | Zbl