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arXiv · 2608.29976

The Pego Theorem for the Hilbert--Schmidt Class

Yaogan Mensah
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Abstract

This paper establishes an operator-theoretic version of Pego's compactness theorem within the framework of quantum harmonic analysis on general locally compact abelian phase spaces. We show that a bounded set of Hilbert-Schmidt operators is precompact if and only if it is uniformly equicontinuous under phase-space shifts and its Fourier-Weyl transform is uniformly equicontinuous on the dual phase space. We provide applications to quantum physics.

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Yaogan Mensah. 2026-08-30. The Pego Theorem for the Hilbert--Schmidt Class. https://arxiv.org/abs/2608.29976

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