On the existence of polyanalytic functions |
| |
Authors: | Luís V Pessoa |
| |
Institution: | Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa |
| |
Abstract: | We give a sharp estimate for the codimension of the poly‐Bergman space in the poly‐Bergman space over the punctured domain. It is established the behaviour at the infinity point of polyanalytic Bergman functions on the complement of closed disks. In the main result of the paper, we prove that for and the j‐polyanalytic Bergman space over the domain U is trivial precisely when the complement of U has at most one point and at most two points or three points lying in a circle, respectively. We point out the differences between the domains over which the Bergman space and the non‐analytic poly‐Bergman space are trivial. |
| |
Keywords: | Poly– Bergman space polyanalytic function logarithmic capacity 30G20 30C85 46E22 |
|
|