On $p$-adic spectral measures

Ruxi Shi

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arXiv · 2002.07559

On $p$-adic spectral measures

Ruxi Shi

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Abstract

A Borel probability measure $\mu$ on a locally compact group is called a spectral measure if there exists a subset of continuous group characters which forms an orthogonal basis of the Hilbert space $L^2(\mu)$. In this paper, we characterize all spectral measures in the field $\mathbb{Q}_p$ of $p$-adic numbers.

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Ruxi Shi. 2020-02-18. On $p$-adic spectral measures. https://arxiv.org/abs/2002.07559

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