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We give here some precisions and improvements about the validity of theexplicit reconstruction of any holomorphic function on a ball of $\mathbb{C}^2$from its restrictions on a family of complex lines. Such validity depends onthe mutual distribution of the lines. This condition can be geometricallydescribed and is equivalent to a stronger stability of the reconstructionformula in terms of permutations and subfamilies of these lines. The motivationof this problem comes from possible applications in mathematical economics andmedical imaging.

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