Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Mensah, Yaogan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204913993