度量三元矩阵分布的极限谱量

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI:10.1134/S0016266323020089

A. M. Vershik, F. V. Petrov

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引用次数: 0

摘要

摘要界定了度量三重（即度量空间）的极限谱度量概念。如果度量是平方可积分的，那么极限谱度量就是确定的，并且与 \(L^2(\mu)\) 上核 \(\rho\) 的积分算子谱重合。我们构建了一个不存在确定谱度量的例子。

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Limit Spectral Measures of Matrix Distributions of Metric Triples

The notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is deterministic and coincides with the spectrum of the integral operator on \(L^2(\mu)\) with kernel \(\rho\). An example in which there is no deterministic spectral measure is constructed.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.