Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space

Ludovic Dan Lemle (1, 2) , Liming Wu (1, 3)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Faculte d'Ingenierie de Hunedoara
3 Department of Mathematics

The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique $L^1(\R^d,dx)$ weak solution.

Mots clés: $C_0$-semigroups; $L^\infty$-uniqueness; mass transport equation

Domaines: Analyse fonctionnelle [math.FA]

Ludovic Dan Lemle, Liming Wu. Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space. 2006. ⟨hal-00197494⟩