Geometric conditions for the reconstruction of a holomorphic function by interpolation formula

Details Geometric conditions for the reconstruction of a holomorphic function by interpolation formula Geometric conditions for the reconstruction of a holomorphic function by interpolation formula

2011-07-29

arxiv.org/abs/1108.0008v1

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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