1. Boundary functions on a bounded balanced domain
- Creator:
- Kot, Piotr
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- boundary behavior of holomorphic functions, exceptional sets, boundary functions, Dirichlet problem, and Radon inversion problem
- Language:
- English
- Description:
- We solve the following Dirichlet problem on the bounded balanced domain $\Omega $ with some additional properties: For $p>0$ and a positive lower semi-continuous function $u$ on $\partial \Omega $ with $u(z)=u(\lambda z)$ for $|\lambda |=1$, $z\in \partial \Omega $ we construct a holomorphic function $f\in \Bbb O(\Omega )$ such that $u(z)=\int _{\Bbb Dz}|f|^pd \frak L_{\Bbb Dz}^2$ for $z\in \partial \Omega $, where $\Bbb D=\{\lambda \in \Bbb C\:|\lambda |<1\}$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public