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arXiv · 2308.01107

Function Theory off the complexified unit circle: Fr\'echet space structure and automorphisms

Michael Heins·Annika Moucha·Oliver Roth
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Abstract

Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fr\'echet space structure of the set of holomorphic functions on the complement $\Omega:=\{(z,w)\in \hat{\mathbb{C}}^2\, :\, z\cdot w\not=1\}$ of the complexified unit circle ${\{(z,w) \in \hat{\mathbb{C}}^2 \, : \, z\cdot w=1\}}$. We also characterize the subgroup of all biholomorphic automorphisms of $\Omega$ which leave the canonical Laplacian on $\Omega$ invariant.

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Michael Heins, Annika Moucha, Oliver Roth. 2023-08-02. Function Theory off the complexified unit circle: Fr\'echet space structure and automorphisms. https://doi.org/10.54330/afm.144880

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