Geodesic
Boundary functions in $L^2H(\mathbb{B}^n)$
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 29-47 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 \[ u(z)=\int _{|\lambda |1}\left|f(\lambda z)\right|^{2}\mathrm{d}{\mathfrak L}^{2}(\lambda ). \]
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 \[ u(z)=\int _{|\lambda |1}\left|f(\lambda z)\right|^{2}\mathrm{d}{\mathfrak L}^{2}(\lambda ). \]
Classification : 30B30, 32A10, 32A40
Keywords: boundary behavior of holomorphic functions; exceptional sets; boundary functions; computed tomography; Dirichlet problem 
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Kot, Piotr. Boundary functions in $L^2H(\mathbb{B}^n)$. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 29-47. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a2/

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