Geodesic
Function theory off the complexified unit circle: Fréchet space structure and automorphisms
Michael Heins1 ; Annika Moucha1 ; Oliver Roth1
1University of Würzburg, Department of Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 257–280

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Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fréchet space structure of the set of holomorphic functions on the complement $\Omega:=\{(z,w)\in \hat{\mathbb{C}}^2\colon z\cdot w\not=1\}$ of the complexified unit circle $\{(z,w) \in \hat{\mathbb{C}}^2 \colon z\cdot w=1\}$. We also characterize the subgroup of all biholomorphic automorphisms of $\Omega$ which leave the canonical Laplacian on $\Omega$ invariant.
DOI : 10.54330/afm.144880
Keywords: Schauder basis, invariant Laplacian, conformal invariance

Michael Heins  1   ; Annika Moucha  1   ; Oliver Roth  1

1 University of Würzburg, Department of Mathematics 
Michael Heins; Annika Moucha; Oliver Roth. Function theory off the complexified unit circle: Fréchet space structure and automorphisms. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 257–280. doi: 10.54330/afm.144880
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