闭流形上的全局特征族

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-25 DOI:10.1112/jlms.70228

Oskar Riedler, Anna Siffert

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引用次数: 0

摘要

研究了闭黎曼流形上全局定义的（λ, μ） $(\lambda,\mu)$ -特征族。其中，我们提供了这些特征族的（不）存在性结果，检查了特征族存在的拓扑结果，并在平坦环面上分类了（λ, μ） $(\lambda,\mu)$ -特征族。进一步证明，当f = f 1 + i f 2 $f=f_1+i f_2$是一个分解为实部和虚部的特征函数时，幂{ f 1a f 2b∣a, b∈N }$\lbrace f_1^a f_2^b\mid a,b\in \mathbb N\rbrace$在l2 (M) $L^2(M)$中满足高度刚性正交关系。在建立这些正交关系的过程中，我们得到了包含二项乘积的行列式的组合恒等式，我们认为这是一个独立的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Global eigenfamilies on closed manifolds

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Global eigenfamilies on closed manifolds

We study globally defined $(λ, μ)$ -eigenfamilies on closed Riemannian manifolds. Among others, we provide (non-)existence results for such eigenfamilies, examine topological consequences of the existence of eigenfamilies and classify $(λ, μ)$ -eigenfamilies on flat tori. It is further shown that for $f = f_{1} + i f_{2}$ being an eigenfunction decomposed into its real and its imaginary part, the powers ${f_{1}^{a} f_{2}^{b} ∣ a, b \in N}$ satisfy highly rigid orthogonality relations in $L^{2} (M)$ . In establishing these orthogonality relations, one is led to combinatorial identities involving determinants of products of binomials, which we view as being of independent interest.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.