圆盘Aharonov–Bohm特征值的Pólya型不等式
谱理论
2024-03-21 v2 数学物理
math.MP
摘要
我们证明了圆盘上带Aharonov–Bohm势的磁Schrödinger算子的特征值在Dirichlet与磁Neumann边界条件下的Pólya猜想的类似结果。这回答了R. L. Frank与A. M. Hansson在2008年提出的一个问题。
引用
@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}
}
备注
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