Geodesic
Twisted convolution and Moyal star product of generalized functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 9-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Moyal product, twisted convolution, Weyl–Heisenberg group, noncommutative field theory, topological $*$-algebra, generalized function.
Mots-clés : Weyl symbol 
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M. A. Soloviev. Twisted convolution and Moyal star product of generalized functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 9-27. http://geodesic.mathdoc.fr/item/TMF_2012_172_1_a1/

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