Geodesic
Smooth structure and differential operators on a~locally compact group
Izvestiya. Mathematics , Tome 59 (1995) no. 1, pp. 1-44

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We describe the structure of differential operators (that is, locally linear operators in the space of Bruhat smooth functions) on an arbitrary locally compact group $G$. 
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     author = {S. S. Akbarov},
     title = {Smooth structure and differential operators on a~locally compact group},
     journal = {Izvestiya. Mathematics },
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S. S. Akbarov. Smooth structure and differential operators on a~locally compact group. Izvestiya. Mathematics , Tome 59 (1995) no. 1, pp. 1-44. http://geodesic.mathdoc.fr/item/IM2_1995_59_1_a0/