English

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