Mathematics – Complex Variables
Scientific paper
2011-07-29
Mathematics
Complex Variables
Scientific paper
We give here some precisions and improvements about the validity of the explicit reconstruction of any holomorphic function on $\mathbb{C}^2$ from the knowledge of its restrictions on a family of complex lines. Such a validity depends on the mutual repartition of the lines. This condition can by geometrically described and is equivalent to a stronger stability of the reconstruction formula in terms of permutations and subfamilies of lines. The motivation of this problem also comes from possible applications in mathematical economics and medical imaging.
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