Three short tales on the parity operator
Functional Analysis
2026-03-30 v1
Abstract
In this paper, we discuss three short topics related to the parity operator and his role in quantum harmonic analysis. We derive results for the Fredholm index of even and odd operators, discuss operators on which the modulation action acts continuous in operator norm and show that the parity operator plays a natural role in the operator-to-operator Fourier transform of quantum harmonic analysis.
Cite
@article{arxiv.2603.25939,
title = {Three short tales on the parity operator},
author = {Robert Fulsche},
journal= {arXiv preprint arXiv:2603.25939},
year = {2026}
}