Quantum Hermite functions and Fourier Transform of operators

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Rahul Garg, Sundaram Thangavelu
DOI: 10.48550/arxiv.2602.12626
Cited by: 0

Abstract

We construct operator analogues of Hermite functions which form an orthonormal basis for the Hilbert space $ \mathcal{S}_2$ of Hilbert-Schmidt operators on $ L^2(\R^n).$ We use this orthonormal basis to define Fourier transform on $ \mathcal{S}_2 $ and study some of its basic properties.

Fields of Study & Subjects

Mathematical Analysis and Transform Methods Advanced Operator Algebra Research Spectral Theory in Mathematical Physics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
13 February 2026
Language
EN
Document type
Preprint