ORIGINAL RESEARCH article
Front. Phys.
Sec. Quantum Engineering and Technology
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1640681
This article is part of the Research TopicRecent Mathematical and Theoretical Progress in Quantum MechanicsView all 7 articles
MEASURES AND OPERATORS ASSOCIATED TO PARSEVAL DISTRIBUTION FRAMES
Provisionally accepted
Camillo Trapani1,2*
Francesco Tschinke2- 1University of Palermo, Palermo, Italy
- 2Universita degli Studi di Palermo Dipartimento di Matematica e Informatica, Palermo, Italy
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Continuing the study undertaken in \cite{TTT} some more aspects of distribution frames (namely, Gel'fand, Parseval) are examined, with a particular care to those more relevant for applications to quantum physics. Parseval distribution frames are, in particular, closely related to coherent states. Thus, POV-measures, Naimark dilations and operators defined by Parseval distribution frames are the main subjects of the paper.
Keywords: Parseval distribution frames, POV-measures, Naimark dilations, Operators, Rigged Hilbert space
Received: 04 Jun 2025; Accepted: 12 Sep 2025.
Copyright: © 2025 Trapani and Tschinke. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Camillo Trapani, camillo.trapani@unipa.it
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