The surjectivity of the combinatorial Laplacian on infinite graphs
Tullio Ceccherini-Silberstein
Università del Sannio, Benevento, ItalyMichel Coornaert
Université de Strasbourg, FranceJozef Dodziuk
The CUNY Graduate Center, New York, United States
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Abstract
Given a connected locally finite simplicial graph with vertex set , the combinatorial Laplacian is defined on the space of all real-valued functions on . We prove that is surjective if is infinite.
Cite this article
Tullio Ceccherini-Silberstein, Michel Coornaert, Jozef Dodziuk, The surjectivity of the combinatorial Laplacian on infinite graphs. Enseign. Math. 58 (2012), no. 1/2, pp. 125–130
DOI 10.4171/LEM/58-1-5