English

An approximation formula for holomorphic functions by interpolation on the ball

Complex Variables 2008-03-31 v1

Abstract

We deal with a problem of the reconstruction of any holomorphic function ff on the unit ball of C2\mathbb{C}^2 from its restricions on a union of complex lines. We give an explicit formula of Lagrange interpolation's type that is constructed from the knowledge of ff and its derivatives on these lines. We prove that this formula approximates any function when the number of lines increases. The motivation of this problem comes also from possible applications in mathematical economics and medical imaging.

Keywords

Cite

@article{arxiv.0803.4178,
  title  = {An approximation formula for holomorphic functions by interpolation on the ball},
  author = {Amadeo Irigoyen},
  journal= {arXiv preprint arXiv:0803.4178},
  year   = {2008}
}
R2 v1 2026-06-21T10:25:28.889Z