Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock

Maria Trybula

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arXiv · 1304.0252

Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock

Maria Trybula

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Abstract

We consider a proper holomorphic map form D to G domains in C^n and show that it induces a unitary isomorphism between the Bergman space A^2(G) and some subspace of A^2(D). Using this isomorphism we construct orthogonal projection onto that subspace and we derive Bells transformation formula for the Bergman kernel under proper holomorphic mappings. As a consequence of the formula we get that the tetrablock is not a Lu Qi-Keng domain.

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Maria Trybula. 2013-03-31. Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock. https://arxiv.org/abs/1304.0252

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