Inequalities \`a la P\'olya for the Aharonov--Bohm eigenvalues of the disk
Spectral Theory
2024-03-21 v2 Mathematical Physics
math.MP
Abstract
We prove an analogue of P\'olya's conjecture for the eigenvalues of the magnetic Schr\"odinger operator with Aharonov--Bohm potential on the disk, for Dirichlet and magnetic Neumann boundary conditions. This answers a question posed by R. L. Frank and A. M. Hansson in 2008.
Keywords
Cite
@article{arxiv.2311.14072,
title = {Inequalities \`a la P\'olya for the Aharonov--Bohm eigenvalues of the disk},
author = {Nikolay Filonov and Michael Levitin and Iosif Polterovich and David A. Sher},
journal= {arXiv preprint arXiv:2311.14072},
year = {2024}
}
Comments
v2: dedication added, journal's accepted version. 16 pages, 4 figures. A Mathematica script used for a computer-assisted part of the paper and its printout are available for download at https://michaellevitin.net/polya.html#AB