Geodesic
Exceptional Sets in Convex Domains
Journal of convex analysis, Tome 12 (2005) no. 2, pp. 351-364.

Voir la notice de l'article provenant de la source Heldermann Verlag

Assume that $\Omega$ is a strongly convex domain, balanced with boundary of class $C^{1}$. Fix number $p \geq 1$. For any set $E$ which is circular and of type $G_{\delta}$ in $\partial\Omega$ we find a holomorphic function $f\in \mathbb{O}(\Omega)$ such that \[ E=E_{\Omega}^{p}(f)=\left\{ z\in \partial \Omega: \:\int_{|\lambda| 1} \left|f(\lambda z)\right|^{p}d\mathfrak{L}^{2}(\lambda)=\infty\right\} .\]
Classification : 30B30, 30E25
Mots-clés : Boundary behavior of holomorphic functions, exceptional sets, power series, computed tomography 
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     author = {P. Kot},
     title = {Exceptional {Sets} in {Convex} {Domains}},
     journal = {Journal of convex analysis},
     pages = {351--364},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2005},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a6/}
}
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P. Kot. Exceptional Sets in Convex Domains. Journal of convex analysis, Tome 12 (2005) no. 2, pp. 351-364. http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a6/