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.

引用

页数：10

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