The L2 strong maximum principle on arbitrary countable networks

Autor:	Cardanobile, Stefano
Rok vydání:	2009
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics Mathematics - Functional Analysis 35K05 05C50
Druh dokumentu:	Working Paper
DOI:	10.1016/j.laa.2011.03.001
Popis:	We study the strong maximum principle for the heat equation associated with the Dirichlet form on countable networks. We start by analyzing the boundedness properties of the incidence operators on a countable network. Subsequently, we prove that the strong maximum principle is equivalent to the underlying graph being connected after deletion of the nodes with infinite degree. Using this result, we prove that the number of connected components of the graph with respect to the heat flow equals the number of maximal invariant ideals of the adjacency matrix. Comment: 14 pages; accepted in "Linear algebra and its applications"
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0902.0251 Zobrazit plný text záznamu View this record from Arxiv