Geodesic
On~a~characteristic property of Weyl quantization
Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 3, pp. 292-296

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A condition is found under which a linear continuous mapping $W_1\colon L_2(\mathscr M)\to\hat{L_2}(H)$ of the space $L_2(\mathscr M)$ of generalized functionals on a phase space $\mathscr M$ into the set $\hat{L_2}(H)$ of Hilbert–Schmidt operators on a Fok space $H$ differs by only a numerical factor from Weyl quantization $W$. 
@article{TMF_1970_2_3_a1,
     author = {V. S. Buslaev and M. M. Skriganov},
     title = {On~a~characteristic property of {Weyl} quantization},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {292--296},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a1/}
}
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V. S. Buslaev; M. M. Skriganov. On~a~characteristic property of Weyl quantization. Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 3, pp. 292-296. http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a1/