2012/07/01 by M. A. Soloviev, Michael A. Soloviev · 11 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Computer science #Convolution (computer science) #Convolution theorem #Dual space #Fourier analysis #Fourier transform #Fractional Fourier transform #Generalized function #Geometry #Heisenberg group #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Multiplier (economics) #Noncommutative and Quantum Gravity Theories #Product (mathematics) #Pure mathematics #Space (punctuation) #Star (game theory) #Star product #hep-th #math-ph #math.FA #math.MP #msc:46E25 #msc:46F05 #msc:46F10 #msc:46L65 #msc:53D55
paper · pdf · doi:10.1007/s11232-012-0084-8
published in Theoretical and Mathematical Physics 172(1), 885-900 (Pleiades Publishing) · LaTeX, 16 pages, no figures
openalex publication_date 2012/07/01 · arxiv created 2012/08/09 · arxiv updated 2012/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.