Spectral Estimates over Multiply Connected Domains

Georgios Tsikalas

Spectral Estimates over Multiply Connected Domains

Functional Analysis 2026-07-11 v1 Complex Variables

Authors: Georgios Tsikalas

Abstract

We consider the quantum analogue of a disk with $n$ pairwise disjoint circular holes. We establish a uniform upper bound for the associated spectral constant that is independent of the geometry of the holes, together with a sharper asymptotic bound when the holes are well-separated. The latter generalizes recent estimates for the quantum annulus due to Crouzeix and Pascoe.

Cite

@article{arxiv.2607.10107,
  title  = {Spectral Estimates over Multiply Connected Domains},
  author = {Georgios Tsikalas},
  journal= {arXiv preprint arXiv:2607.10107},
  year   = {2026}
}