Boundary functions in $L^2H(\mathbb{B}^n)$

Title:

Boundary functions in $L^2H(\mathbb{B}^n)$

Creator:

Kot, Piotr

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:03047a7f-30e1-4650-abe4-d21f2b03cf07
uuid:03047a7f-30e1-4650-abe4-d21f2b03cf07

Subject:

boundary behavior of holomorphic functions, exceptional sets, boundary functions, computed tomography, and Dirichlet problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball: For a function $u$ which is lower semi-continuous on $\partial \mathbb{B}^{n}$ we give necessary and sufficient conditions in order that there exists a holomorphic function $f\in \mathbb{O}(\mathbb{B}^{n})$ such that \[ u(z)=\int _{|\lambda |<1}\left|f(\lambda z)\right|^{2}\mathrm{d}{\mathfrak L}^{2}(\lambda ).\].

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

29-47

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:1

Harvested from:

CDK

Metadata only:

false