Some spectral comparison results on infinite quantum graphs

Abstract

In this paper we establish spectral comparison results for Schrödinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting. We also show that new features do appear on infinite quantum graphs such as a modified local Weyl law. In this sense, we regard this paper as a starting point for a more thorough investigation of spectral comparison results on more general infinite metric graphs.

11 pages, 3 figures, comments welcome!

References in corpus (4)

• Comparing the spectrum of Schrödinger operators on quantum graphs
• Differences between Robin and Neumann eigenvalues on metric graphs
• A note on Ambarzumian's theorem for quantum graphs
• Towards a theory of eigenvalue asymptotics on infinite metric graphs: the case of diagonal combs

Cited by in corpus (1)

• A modified local Weyl law and spectral comparison results for ${\delta }^{\prime }$-coupling conditions