Interpolation Formulas With Derivatives in De Branges Spaces II

TL;DR

This paper explores conditions for reconstructing entire functions in de Branges spaces from both function values and derivatives, focusing on spaces with bounded logarithmic derivatives in the upper half-plane.

Contribution

It provides necessary and sufficient conditions for interpolation with derivatives in de Branges spaces with specific structural properties.

Findings

Characterization of interpolation formulas with derivatives in de Branges spaces.

Conditions for reconstructing functions from values and derivatives.

Analysis of spaces with bounded logarithmic derivatives.

Abstract

We investigate necessary and sufficient conditions under which entire functions in de Branges spaces can be recovered from function values and values of derivatives. Our main focus is on spaces with a structure function whose logarithmic derivative is bounded in the upper half-plane.