Graph Laplacians do not generate strongly continuous semigroups

Abstract

We show that for graph Laplacians ${\Delta }_G$ on a connected locally finite simplicial undirected graph $G$ with countable infinite vertex set $V$ none of the operators $\alpha \mathrm{Id}+\beta {\Delta }_G,\alpha ,\beta \in \mathbb{K},\beta \ne 0$, generate a strongly continuous semigroup on ${\mathbb{K}}^V$ when the latter is equipped with the product topology.

3 pages

References in corpus (1)

• Strongly continuous semigroups on some Fréchet spaces