PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{mensah2026pego,
title = {{The Pego Theorem for the Hilbert--Schmidt Class}},
author = {Yaogan Mensah},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29976},
eprint = {2608.29976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29976},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Pego Theorem for the Hilbert--Schmidt Class
AU - Yaogan Mensah
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29976
UR - https://arxiv.org/abs/2608.29976
AB - 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.
ER -