A criterion for the explicit reconstruction of a holomorphic function from its restrictions on lines

TL;DR

This paper investigates a criterion for explicitly reconstructing a holomorphic function in two complex variables from its values on a union of lines, with implications for economics and medical imaging.

Contribution

It provides an analytical condition on the arrangement of lines that guarantees successful explicit reconstruction of the holomorphic function.

Findings

Reconstruction depends on the mutual arrangement of lines

Established an analytical criterion for line configurations

Potential applications in economics and medical imaging

Abstract

We deal with a problem of the explicit reconstruction of any holomorphic function $f$ on $\mathbb{C}^2$ from its restricions on a union of complex lines. The validity of such a reconstruction essentially depends on the mutual repartition of these lines, condition that can be analytically described. The motivation of this problem comes also from possible applications in mathematical economics and medical imaging.