A non-uniform Datko-Pazy theorem for bounded operator semigroups
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910612484784128 |
|---|---|
| author | Paunonen, Lassi Seifert, David Vanspranghe, Nicolas |
| author_facet | Paunonen, Lassi Seifert, David Vanspranghe, Nicolas |
| contents | We present a non-uniform analogue of the classical Datko-Pazy theorem. Our main result shows that an integrability condition imposed on orbits originating in a fractional domain of the generator (as opposed to all orbits) implies polynomial stability of a bounded $C_0$-semigroup. As an application of this result we establish polynomial stability of a semigroup under a certain non-uniform Lyapunov-type condition. We moreover give a new proof, under slightly weaker assumptions, of a recent result deducing polynomial stability from a certain non-uniform observability condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-uniform Datko-Pazy theorem for bounded operator semigroups Paunonen, Lassi Seifert, David Vanspranghe, Nicolas Functional Analysis We present a non-uniform analogue of the classical Datko-Pazy theorem. Our main result shows that an integrability condition imposed on orbits originating in a fractional domain of the generator (as opposed to all orbits) implies polynomial stability of a bounded $C_0$-semigroup. As an application of this result we establish polynomial stability of a semigroup under a certain non-uniform Lyapunov-type condition. We moreover give a new proof, under slightly weaker assumptions, of a recent result deducing polynomial stability from a certain non-uniform observability condition. |
| title | A non-uniform Datko-Pazy theorem for bounded operator semigroups |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2409.12764 |