Some Applications of Higher-Order Hyperbolic Derivatives

摘要

The notion of higher-order hyperbolic derivatives was recently introduced. As the given definition does not lend to simple calculations, we first give a recursive formula to calculate them, which may be useful for a possible numerical use. Next, as a first application of hyperbolic derivatives of higher order, we develop some tools for solving a particular interpolation problem involving them and which allow us to consider the constrained Nevanlinna-Pick problem. Finally, we generalize and interpret some classical results of complex analysis in this new setting: Dieudonné's Lemma and Rogosinski's Lemma.