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arXiv · 1412.5854

A short remark on the surjectivity of the combinatorial Laplacian on infinite graphs

Thomas Kalmes
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Abstract

Applying a well-known theorem due to Eidelheit, we give a short proof of the surjectivity of the combinatorial Laplacian on connected locally finite undirected simplicial graph $G$ with countably infinite vertex set $V$, established by Ceccherini-Silberstein, Coornaert, and Dodziuk. In fact, we show that every linear operator on $\mathbb{K}^V$ which has finite hopping range and satisfies the pointwise maximum principle is surjective.

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Thomas Kalmes. 2014-12-18. A short remark on the surjectivity of the combinatorial Laplacian on infinite graphs. https://doi.org/10.1007/s13398-015-0258-y

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