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Keywords:
boundary behavior of holomorphic functions; exceptional sets; boundary functions; computed tomography; Dirichlet problem
boundary behavior of holomorphic functions; exceptional sets; boundary functions; computed tomography; Dirichlet problem
Summary:
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 \[ u(z)=\int _{|\lambda |<1}\left|f(\lambda z)\right|^{2}\mathrm{d}{\mathfrak L}^{2}(\lambda ). \]
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