TY - UNPB
T1 - Limit-case admissibility for positive infinite-dimensional systems
AU - Arora, Sahiba
AU - Glück, Jochen
AU - Paunonen, Lassi
AU - Schwenninger, Felix L.
N1 - 30 pages, corrected minor typos, added Remark 3.6, minor correction to Example 5.2
PY - 2024/4/1
Y1 - 2024/4/1
N2 - 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.
AB - 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.
KW - math.FA
U2 - 10.48550/arXiv.2404.01275
DO - 10.48550/arXiv.2404.01275
M3 - Preprint
BT - Limit-case admissibility for positive infinite-dimensional systems
PB - ArXiv.org
ER -