Norms, Kernels and Eigenvalues of some Infinite Graphs

2018/12/19 by Agrawal, Aahan, Berge, Astrid, Colbert-Pollack, Seth +2
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1812.08276

Abstract

In these paper we study the adjacency matrix of some infinite graphs, which we call the shift operator on the L^p space of the graph. In particular, we establish norm estimates, we find the norm for some cases, we decide the triviality of the kernel of some infinite trees, and we find the eigenvalues of certain infinite graphs obtained by attaching an infinite tail to some finite graphs.

Related

• Spectra of infinite graphs with tails
• Spectra of infinite graphs: two methods of computation
• Eigenvalues and extremal degrees in graphs
• Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs
• The dual Cheeger constant and spectra of infinite graphs