Domains of uniqueness for $C_0$-semigroups on the dual of a Banach space
| dc.creator | Lemle, Ludovic Dan | |
| dc.date | 2008-06-09 | |
| dc.date.accessioned | 2026-07-07T12:19:24Z | |
| dc.date.available | 2026-07-07T12:19:24Z | |
| dc.description | Let $({\cal X},\|\:.\:\|)$ be a Banach space. In general, for a $C_0$-semigroup \semi on $({\cal X},\|\:.\:\|)$, its adjoint semigroup \semia is no longer strongly continuous on the dual space $({\cal X}^{*},\|\:.\:\|^{*})$. Consider on ${\cal X}^{*}$ the topology of uniform convergence on compact subsets of $({\cal X},\|\:.\:\|)$ denoted by ${\cal C}({\cal X}^{*},{\cal X})$, for which the usual semigroups in literature becomes $C_0$-semigroups. The main purpose of this paper is to prove that only a core can be the domain of uniqueness for a $C_0$-semigroup on $({\cal X}^{*},{\cal C}({\cal X}^{*},{\cal X}))$. As application, we show that the generalized Schrödinger operator ${\cal A}^Vf={1/2}Δf+b\cdot\nabla f-Vf$, $f\in C_0^\infty(\R^d)$, is $L^\infty(\R^d,dx)$-unique. Moreover, we prove the $L^1(\R^d,dx)$-uniqueness of weak solution for the Fokker-Planck equation associated with ${\cal A}^V$. | |
| dc.identifier | https://arxiv.org/abs/0806.1428 | |
| dc.identifier | http://arxiv.org/abs/0806.1428 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212743 | |
| dc.subject | Mathematical Physics | |
| dc.title | Domains of uniqueness for $C_0$-semigroups on the dual of a Banach space | |
| dc.type | text |