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Proper holomorphic mappings vs. peak points and Shilov boundary

Łukasz Kosiński, Włodzimierz Zwonek (2013)

Annales Polonici Mathematici

We present a result on the existence of some kind of peak functions for ℂ-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for A(D) under proper holomorphic mappings. Additionally, we present a description of the set of peak points in the class of bounded pseudoconvex Reinhardt domains.

Regular holomorphic images of balls

John Erik Fornaess, Edgar Lee Stout (1982)

Annales de l'institut Fourier

Every n -dimensional complex manifold (connected, paracompact and Hausdorff) is the image of the unit ball in C n under a finite holomorphic map that is locally biholomorphic.

Reproducing properties and L p -estimates for Bergman projections in Siegel domains of type II

David Békollé, Anatole Temgoua Kagou (1995)

Studia Mathematica

On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted L p -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some L p -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space A 2 .

Currently displaying 121 – 140 of 205