Spectral properties of dynamical tensor powers, and tensor factorizations of simple Lebesgue spectrum
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914833074487296 |
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| author | Ryzhikov, Valery V. |
| author_facet | Ryzhikov, Valery V. |
| contents | For every $n>0$ there is a unitary operator $U$ such that the unitary operator with simple Lebesgue spectrum is isomorphic to the tensor product $U\otimes U^2\otimes\dots\otimes U^{2^n}.$ There is an ergodic automorphism $T$ with its symmetric tensor power $T^{\odot n}$ of simple spectrum, and $T^{\odot(n+1)}$ of absolutely continuous spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral properties of dynamical tensor powers, and tensor factorizations of simple Lebesgue spectrum Ryzhikov, Valery V. Dynamical Systems For every $n>0$ there is a unitary operator $U$ such that the unitary operator with simple Lebesgue spectrum is isomorphic to the tensor product $U\otimes U^2\otimes\dots\otimes U^{2^n}.$ There is an ergodic automorphism $T$ with its symmetric tensor power $T^{\odot n}$ of simple spectrum, and $T^{\odot(n+1)}$ of absolutely continuous spectrum. |
| title | Spectral properties of dynamical tensor powers, and tensor factorizations of simple Lebesgue spectrum |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2406.08409 |