Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock
Complex Variables
2013-04-02 v1
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.
Keywords
Cite
@article{arxiv.1304.0252,
title = {Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock},
author = {Maria Trybula},
journal= {arXiv preprint arXiv:1304.0252},
year = {2013}
}
Comments
6 pages