Inequalities \`a la P\'olya for the Aharonov--Bohm eigenvalues of the disk
Nikolay Filonov, Michael Levitin, Iosif Polterovich, and David A. Sher
TL;DR
This paper establishes a Pólya-type inequality for the eigenvalues of the magnetic Schrödinger operator with Aharonov--Bohm potential on the disk, addressing a question from 2008 and extending spectral inequalities to magnetic settings.
Contribution
It proves a Pólya-type inequality for Aharonov--Bohm eigenvalues on the disk, filling a gap in spectral theory for magnetic operators.
Findings
Proved Pólya's conjecture analogue for magnetic eigenvalues
Extended spectral inequalities to magnetic Schrödinger operators
Answered a longstanding open question from 2008
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.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems