TL;DR
This paper explores the mathematical properties and roles of the parity operator in quantum harmonic analysis, including index theory, operator continuity, and Fourier transforms.
Contribution
It introduces new results on the Fredholm index, operator continuity, and the Fourier transform involving the parity operator in quantum harmonic analysis.
Findings
Derived the Fredholm index for even and odd operators
Analyzed the continuity of modulation action on certain operators
Showed the parity operator's role in operator-to-operator Fourier transform
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.