Inequalities à la Pólya for the Aharonov--Bohm eigenvalues of the disk

Abstract

We prove an analogue of Pólya's conjecture for the eigenvalues of the magnetic Schrödinger 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.

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

Cited by in corpus (1)

• Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field on disks in the strong field limit