关于本征函数线性组合的库朗节点域性质，第二部分
摘要
推广库朗节点域定理，“扩展库朗性质”是指前 个本征函数的线性组合至多具有 个节点域。在先前的一篇论文中（Documenta Mathematica, 2018, Vol. 23, pp. 1561--1585），我们给出了该性质的一些简单反例，包括凸区域。在本文中，利用数值计算的一些输入，我们通过两个新例子——等边菱形和正六边形——继续研究扩展库朗性质。
引用
@article{arxiv.1803.00449,
title = {On Courant's nodal domain property for linear combinations of eigenfunctions, Part II},
author = {Pierre Bérard and Bernard Helffer},
journal= {arXiv preprint arXiv:1803.00449},
year = {2022}
}
备注
This version differs notably from arXiv 1803.00449v2 (15 Jun 2018). The part concerning Gelfand's approach to Sturm's 1D theorem has been removed (it is developed in arXiv:1807.03990 and will appear in the Moscow Math. Journal). The treatment of Sturm's 1D theorem in the periodic case has been removed. The short paragraph on product-like constructions has been removed as well. A section concerning the hexagon has been added. Minor changes with respect to hal-01718768, version 3 (7 Jun 2019). The paper focuses on the Extended Courant property for the equilateral rhombus and the regular hexagon. Accepted for publication in a forthcoming ''Erick Balslev Memorial Volume'' edited by Sergio Albeverio and Ricardo Weder