The surjectivity of the combinatorial Laplacian on infinite graphs

Tullio Ceccherini-Silberstein, Michel Coornaert, Jozef Dodziuk

Given a connected locally finite simplicial graph $G$ with vertex set $V$, the combinatorial Laplacian ${\Delta }_G:{\mathbb{R}}^V\to {\mathbb{R}}^V$ is defined on the space of all real-valued functi…