Thomas Kalmes, Christoph Schumacher: Graph Laplacians do not generate strongly continuous semigroups

Author(s):

Thomas Kalmes
Christoph Schumacher

Title:

Thomas Kalmes, Christoph Schumacher: Graph Laplacians do not generate strongly continuous semigroups

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 16, 2015

Mathematics Subject Classification:

    47D06 []
    05C63 []
    46A04 []

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 $\alpha\,\Id+\beta\Delta_G, \alpha,\beta\in\K,\beta\ne0$, generate a strongly continuous semigroup on $\K^V$ when the latter is equipped with the product topology.

Keywords:

graph Laplacians, strongly continuous semigroup on locally convex spaces

Language:

English

Publication time:

08/2015