The surjectivity of the combinatorial Laplacian on infinite graphs
Analysis of PDEs
2012-09-25 v1 Combinatorics
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
@article{arxiv.1103.4901,
title = {The surjectivity of the combinatorial Laplacian on infinite graphs},
author = {Tullio Ceccherini-Silberstein and Michel Coornaert and Jozef Dodziuk},
journal= {arXiv preprint arXiv:1103.4901},
year = {2012}
}