Sub-Linear Growth of a Special Class of $C_0$-Groups on Dense Subsets
We consider a special class of linearly growing $C_0$-groups from [20,24], whose generators are essentially nonselfadjoint unbounded operators. More precisely, these generators have pure point imaginary spectrum, clustering at $ i\infty$, and corresponding dense and minimal, but not uniformly minima...
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| Datum: | 2025 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1116 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | We consider a special class of linearly growing $C_0$-groups from [20,24], whose generators are essentially nonselfadjoint unbounded operators. More precisely, these generators have pure point imaginary spectrum, clustering at $ i\infty$, and corresponding dense and minimal, but not uniformly minimal family of eigenvectors, hence this family do not form a Schauder basis. We obtain sharp two-sided estimates for the norms of $C_0$-groups from this class on dense subsets of a phase space, namely, on $D(A^k)$ for any $k\in\mathbb{N},$ where $A$ is the unbounded generator of the corresponding $C_0$-group. Thereby we prove that these $C_0$-groups have sub-linear growth on $D(A^k)$. This yields the sub-linear growth of classical and all more regular solutions of the Cauchy problems for the corresponding abstract linear evolution equations.
Mathematical Subject Classification 2020: 47D06, 34G10, 46B45, 34K25 |
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