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Spectral synthesis of the invariant Laplacian and complexified spherical harmonics
Annika Moucha
We show that the space of holomorphic functions , where , possesses an orthogonal Sch…
Spectral theory of the invariant Laplacian on the disk and the sphere -- a complex analysis approach
Annika Moucha, Oliver Roth, Michael Heins
The central theme of this paper is the holomorphic spectral theory of the canonical Laplace operator of the complement $Ω:= \{(z,w) \in \widehat{\mathbb{C}}^2 \colon z \cdot w \neq…
Function Theory off the complexified unit circle: Fréchet space structure and automorphisms
Michael Heins, Annika Moucha, Oliver Roth
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…
Peschl-Minda derivatives and convergent Wick star products on the disk, the sphere and beyond
Michael Heins, Annika Moucha, Oliver Roth +1
We introduce and study invariant differential operators acting on the space of holomorphic functions on the complement ${Ω=\{(z,w) \in \hat{\mathbb{C}}^2 \, : \, z…