Limit-case admissibility for positive infinite-dimensional systems
| Autor: | Arora, Sahiba, Glück, Jochen, Paunonen, Lassi, Schwenninger, Felix L. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4064/sm230710-27-2 |
| Popis: | In the context of positive infinite-dimensional linear systems, we systematically study $L^p$-admissible control and observation operators with respect to the limit-cases $p=\infty$ and $p=1$, respectively. This requires an in-depth understanding of the order structure on the extrapolation space $X_{-1}$, which we provide. These properties of $X_{-1}$ also enable us to discuss when zero-class admissibility is automatic. While those limit-cases are the weakest form of admissibility on the $L^p$-scale, it is remarkable that they sometimes follow from order theoretic and geometric assumptions. Our assumptions on the geometries of the involved spaces are minimal. Comment: 30 pages, corrected minor typos, added Remark 3.6, minor correction to Example 5.2 |
| Databáze: | arXiv |
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