The L-system representation and c-entropy
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913668631887872 |
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| author | Belyi, Sergey Makarov, Konstantin A. Tsekanovskii, Eduard |
| author_facet | Belyi, Sergey Makarov, Konstantin A. Tsekanovskii, Eduard |
| contents | Given a symmetric operator $\dot A$ with deficiency indices $(1,1)$ and its self-adjoint extension $A$ in a Hilbert space $\mathcal{H}$, we construct a (unique) L-system with the main operator in $\mathcal{H}$ such that its impedance mapping coincides with the Weyl-Titchmarsh function $M_{(\dot A, A)}(z)$ or its linear-fractional transformation $M_{(\dot A, A_α)}(z)$. Similar L-system constructions are provided for the Weyl-Titchmarsh function $aM_{(\dot A, A)}(z)$ with $a>0$. We also evaluate c-entropy and the main operator dissipation coefficient for the obtained L-systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06828 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The L-system representation and c-entropy Belyi, Sergey Makarov, Konstantin A. Tsekanovskii, Eduard Spectral Theory Primary 47A10, Secondary 47N50 Given a symmetric operator $\dot A$ with deficiency indices $(1,1)$ and its self-adjoint extension $A$ in a Hilbert space $\mathcal{H}$, we construct a (unique) L-system with the main operator in $\mathcal{H}$ such that its impedance mapping coincides with the Weyl-Titchmarsh function $M_{(\dot A, A)}(z)$ or its linear-fractional transformation $M_{(\dot A, A_α)}(z)$. Similar L-system constructions are provided for the Weyl-Titchmarsh function $aM_{(\dot A, A)}(z)$ with $a>0$. We also evaluate c-entropy and the main operator dissipation coefficient for the obtained L-systems. |
| title | The L-system representation and c-entropy |
| topic | Spectral Theory Primary 47A10, Secondary 47N50 |
| url | https://arxiv.org/abs/2306.06828 |