Limit-case admissibility for positive infinite-dimensional systems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909946835107840 |
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| author | Arora, Sahiba Glück, Jochen Paunonen, Lassi Schwenninger, Felix L. |
| author_facet | Arora, Sahiba Glück, Jochen Paunonen, Lassi Schwenninger, Felix L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01275 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit-case admissibility for positive infinite-dimensional systems Arora, Sahiba Glück, Jochen Paunonen, Lassi Schwenninger, Felix L. Functional Analysis 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. |
| title | Limit-case admissibility for positive infinite-dimensional systems |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.01275 |