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arXiv · 2306.14883

Limit spectral measures of matrix distributions of metric triples

A. Vershik·F. Petrov
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Abstract

A 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 coinsides with the spectrum of the integral operator in $L^2(\mu)$ with kernel $\rho$. We construct an example in which there is no deterministic spectral measure.

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A. Vershik, F. Petrov. 2023-06-26. Limit spectral measures of matrix distributions of metric triples. https://arxiv.org/abs/2306.14883

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