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

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

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