Spectral comparison results for Laplacians on discrete graphs
Abstract
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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
advanced mathematical theories
Graph theory and applications
Publication details
- Journal / source
- Archiv der Mathematik
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 1 September 2026
- Language
- EN