Fatou's interpolation theorem implies the Rudin-Carleson theorem

TL;DR

This paper demonstrates that the Rudin-Carleson interpolation theorem can be directly derived from Fatou's older interpolation theorem, establishing a clear logical connection between these two fundamental results in complex analysis.

Contribution

It shows that the Rudin-Carleson theorem is a corollary of Fatou's interpolation theorem, simplifying the understanding of their relationship.

Findings

Rudin-Carleson theorem follows directly from Fatou's theorem

Simplifies the proof of the Rudin-Carleson theorem

Establishes a logical link between two classical theorems

Abstract

The purpose of this paper is to show that the Rudin-Carleson interpolation theorem is a direct corollary of Fatou's much older interpolation theorem (of 1906).