The surjectivity of the combinatorial Laplacian on infinite graphs

Details The surjectivity of the combinatorial Laplacian on infinite graphs The surjectivity of the combinatorial Laplacian on infinite graphs

2011-03-25

arxiv.org/abs/1103.4901v1

Mathematics

Analysis of PDEs

Scientific paper

Given a connected locally finite simplicial graph $ G$ with vertex set $V$,
the combinatorial Laplacian $\Delta_G \colon \R^V \to \R^V$ is defined on the
space of all real-valued functions on $V$. We prove that $\Delta_G$ is
surjective if $G$ is infinite.

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