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Quantum Harmonic Analysis on Locally Compact Abelian Groups

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Robert Fulsche
  • Niklas Galke

Research Organisations

External Research Organisations

  • Autonomous University of Barcelona (UAB)

Details

Original languageEnglish
Article number13
Number of pages58
JournalJournal of Fourier Analysis and Applications
Volume31
Issue number1
Early online date10 Feb 2025
Publication statusPublished - 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

Cite this

Quantum Harmonic Analysis on Locally Compact Abelian Groups. / Fulsche, Robert; Galke, Niklas.
In: Journal of Fourier Analysis and Applications, Vol. 31, No. 1, 13, 02.2025.

Research output: Contribution to journalArticleResearchpeer review

Fulsche R, Galke N. Quantum Harmonic Analysis on Locally Compact Abelian Groups. Journal of Fourier Analysis and Applications. 2025 Feb;31(1):13. Epub 2025 Feb 10. doi: 10.1007/s00041-024-10140-9
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