Details
Original language | English |
---|---|
Article number | 13 |
Number of pages | 58 |
Journal | Journal of Fourier Analysis and Applications |
Volume | 31 |
Issue number | 1 |
Early online date | 10 Feb 2025 |
Publication status | Published - Feb 2025 |
Abstract
We extend the notions of quantum harmonic analysis, as introduced in R. Werner’s paper from 1984 (J Math Phys 25(5):1404–1411), to abelian phase spaces, by which we mean a locally compact abelian group endowed with a Heisenberg multiplier. In this way, we obtain a joint harmonic analysis of functions and operators for each such phase space. Throughout, we spend significant extra effort to include also phase spaces which are not second countable. We obtain most results from Werner’s paper for these general phase spaces, up to Wiener’s approximation theorem for operators. In addition, we extend certain of those results (most notably Wiener’s approximation theorem) to operators acting on certain coorbit spaces affiliated with the phase space.
Keywords
- Locally compact abelian group, Operator convolution, Quantum harmonic analysis
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Fourier Analysis and Applications, Vol. 31, No. 1, 13, 02.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantum Harmonic Analysis on Locally Compact Abelian Groups
AU - Fulsche, Robert
AU - Galke, Niklas
N1 - Publisher Copyright: © The Author(s) 2025.
PY - 2025/2
Y1 - 2025/2
N2 - We extend the notions of quantum harmonic analysis, as introduced in R. Werner’s paper from 1984 (J Math Phys 25(5):1404–1411), to abelian phase spaces, by which we mean a locally compact abelian group endowed with a Heisenberg multiplier. In this way, we obtain a joint harmonic analysis of functions and operators for each such phase space. Throughout, we spend significant extra effort to include also phase spaces which are not second countable. We obtain most results from Werner’s paper for these general phase spaces, up to Wiener’s approximation theorem for operators. In addition, we extend certain of those results (most notably Wiener’s approximation theorem) to operators acting on certain coorbit spaces affiliated with the phase space.
AB - We extend the notions of quantum harmonic analysis, as introduced in R. Werner’s paper from 1984 (J Math Phys 25(5):1404–1411), to abelian phase spaces, by which we mean a locally compact abelian group endowed with a Heisenberg multiplier. In this way, we obtain a joint harmonic analysis of functions and operators for each such phase space. Throughout, we spend significant extra effort to include also phase spaces which are not second countable. We obtain most results from Werner’s paper for these general phase spaces, up to Wiener’s approximation theorem for operators. In addition, we extend certain of those results (most notably Wiener’s approximation theorem) to operators acting on certain coorbit spaces affiliated with the phase space.
KW - Locally compact abelian group
KW - Operator convolution
KW - Quantum harmonic analysis
UR - http://www.scopus.com/inward/record.url?scp=85219203373&partnerID=8YFLogxK
U2 - 10.1007/s00041-024-10140-9
DO - 10.1007/s00041-024-10140-9
M3 - Article
AN - SCOPUS:85219203373
VL - 31
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
SN - 1069-5869
IS - 1
M1 - 13
ER -