Rate of convergence for eigenfunctions of Aharonov-Bohm operators with a moving pole

TL;DR

This paper investigates how eigenfunctions of Aharonov-Bohm operators with a moving pole converge, providing precise estimates for the convergence rate as the pole's position varies within a domain.

Contribution

It offers a sharp estimate for the convergence rate of eigenfunctions of Aharonov-Bohm operators with a moving pole, advancing understanding of their behavior.

Findings

Established a sharp estimate for eigenfunction convergence rate

Analyzed eigenfunctions with half-integer circulation

Focused on operators with Dirichlet boundary conditions

Abstract

We study the behavior of eigenfunctions for magnetic Aharonov-Bohm operators with half-integer circulation and Dirichlet boundary conditions in a planar domain. We prove a sharp estimate for the rate of convergence of eigenfunctions as the pole moves in the interior of the domain.