Geodesic
Operational calculus on a~complex semisimple Lie group
Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 881-916

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For every complex semisimple Lie algebra $\mathfrak g$ we construct a so-called operational calculus, which consists in the isomorphic embedding of $\mathfrak g$ along with its associative hull $\mathfrak G$ into a certain algebra of operator polynomials. We investigate the image of $\mathfrak G$ under this embedding; the resulting theorems comprise the algebraic analog of the functional duality theorems of harmonic analysis (theorems of Paley–Wiener type). 
@article{IM2_1969_3_5_a0,
     author = {D. P. Zhelobenko},
     title = {Operational calculus on a~complex semisimple {Lie} group},
     journal = {Izvestiya. Mathematics },
     pages = {881--916},
     publisher = {mathdoc},
     volume = {3},
     number = {5},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a0/}
}
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D. P. Zhelobenko. Operational calculus on a~complex semisimple Lie group. Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 881-916. http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a0/