Work

Spectral comparison results for Laplacians on discrete graphs

Year: 2026

Type: article

Abstract: In the recent literature, various authors have studied spectral comparison results for Schrödinger operators with discrete spectrum in different settings including Euclidean domains and quantum graphs. In this note, we derive such spectral comparison results in a rather general framework for general and possibly infinite discrete graphs. Along the way, we establish a discrete version of the local Weyl law whose proof does neither involve any Tauberian theorem nor the Weyl law as used in the continuous case.

Source: Archiv der Mathematik

DOI: 10.1007/s00013-026-02284-5

Authors: Patrizio Bifulco, Joachim Kerner, Christian Rose

Institutions: FernUniversität in Hagen, University of Potsdam

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Deutsche Forschungsgemeinschaft