The Pego Theorem for the Hilbert--Schmidt Class

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.

Functional Analysis (math.FA); Quantum Physics (quant-ph)

arXiv:2608.29976 [math.FA]

(or arXiv:2608.29976v1 [math.FA] for this version)

https://doi.org/10.48550/arXiv.2608.29976 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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