Geodesic
Spaces of type $S$ and deformation quantization
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 315-336

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We study the properties of the Gelfand–Shilov spaces $S^{b_n}_{a_k}$ in the context of deformation quantization. Our main result is a characterization of their corresponding multiplier algebras with respect to a twisted convolution, which is given in terms of the inclusion relation between these algebras and the duals of the spaces of pointwise multipliers with an explicit description of these functional spaces. The proof of the inclusion theorem essentially uses the equality $S^{b_n}_{a_k}=S^{b_n}\cap S_{a_k}$.
Mots-clés : deformation quantization, Weyl symbol, Weyl symbol
Keywords: Moyal product, multiplier algebra, Gelfand–Shilov spacedeformation quantization, Moyal product, multiplier algebra, Gelfand–Shilov space. 
@article{TMF_2019_201_3_a1,
     author = {M. A. Soloviev},
     title = {Spaces of type $S$ and deformation quantization},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {315--336},
     publisher = {mathdoc},
     volume = {201},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_3_a1/}
}
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M. A. Soloviev. Spaces of type $S$ and deformation quantization. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 315-336. http://geodesic.mathdoc.fr/item/TMF_2019_201_3_a1/