Sign equidistribution of Legendre polynomials

被引：0
|
作者：
Martinez, Angel D. [1 ,2 ]
de Lizaur, Francisco Torres [1 ,2 ]
机构：
[1] Fields Inst, Mississauga, ON, Canada
[2] Univ Toronto Mississauga, Mississauga, ON, Canada
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2023年 / 13卷 / 04期
基金：
加拿大自然科学与工程研究理事会;
关键词：
EIGENFUNCTIONS;
D O I：
10.1007/s13324-023-00821-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove sign equidistribution of Legendre polynomials: the ratio between the lengths of the regions in the interval [-1, 1] where the Legendre polynomial assumes positive versus negative values, converges to one as the degree grows. The proof method also has application to the symmetry conjecture for a basis of eigenfunctions in the sphere.
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页数：10
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