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arXiv · 1905.01650

Exponential factorizations of holomorphic maps

Frank Kutzschebauch·Luca Studer
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Abstract

We show that any element of the special linear group $SL_2(R)$ is a product of two exponentials if the ring $R$ is either the ring of holomorphic functions on an open Riemann surface or the disc algebra. This is sharp: one exponential factor is not enough since the exponential map corresponding to $SL_2(\mathbb{C})$ is not surjective. Our result extends to the linear group $GL_2(R)$.

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Frank Kutzschebauch, Luca Studer. 2019-05-05. Exponential factorizations of holomorphic maps. https://doi.org/10.1112/blms.12294

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