Geodesic
Holomorphic Functions of Exponential Type on Connected Complex Lie Groups
Journal of Lie theory, Tome 29 (2019) no. 4, pp. 1045-107
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Holomorphic functions of exponential type on a complex Lie group G (introduced by Akbarov) form a locally convex algebra, which is denoted by Oexp(G). Our aim is to describe the structure of Oexp(G) in the case when G is connected. The following topics are auxiliary for the claimed purpose but of independent interest:
Classification : 22E10, 22E30, 32A38, 46F05
Mots-clés : Complex Lie group, linear group, holomorphic function of exponential type, Arens-Michael envelope, submultiplicative weight, length function, exponential radical 
@article{JLT_2019_29_4_JLT_2019_29_4_a9,
     author = {O. Yu. Aristov},
     title = {Holomorphic {Functions} of {Exponential} {Type} on {Connected} {Complex} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {1045--107},
     year = {2019},
     volume = {29},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a9/}
}
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O. Yu. Aristov. Holomorphic Functions of Exponential Type on Connected Complex Lie Groups. Journal of Lie theory, Tome 29 (2019) no. 4, pp. 1045-107. http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a9/