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Algebras in Analysis
November 2, 2018 18:05–19:35, Moscow, Lomonosov Moscow State University, room 13-20.

Holomorphic functions of exponential type on connected complex Lie groups

O. Yu. Aristov

Abstract: For each connected complex Lie group $G$, we explicitly describe the algebra of holomorphic functions of exponential type $\mathcal{O}_{exp}(G)$ introduced by Akbarov. The key point is a decomposition of the maximal length function into three summands, which yields a decomposition of $\mathcal{O}_{exp}(G)$ into the projective tensor products of three factors. We also essentially use the exponential radical of $G$. As a corollary, we show that the polynomial functions on $G$ are contained in $\mathcal{O}_{exp}(G)$ if and only if $G$ is linear.