Pseudo-hyperbolic distance and n-best rational approximation in H^2 space

TL;DR

This paper demonstrates the existence of optimal rational approximations in the Hardy H2 space using pseudo-hyperbolic distance, by leveraging the rational orthogonal system known as the Takenaka-Malmquist system.

Contribution

It introduces a new proof for the existence of n-best rational approximations in H2 space utilizing pseudo-hyperbolic distance and the Takenaka-Malmquist system.

Findings

Proof of existence of n-best rational approximation in H2 space

Utilization of pseudo-hyperbolic distance in approximation theory

Application of Takenaka-Malmquist system for rational approximation

Abstract

Through reducing the problem to rational orthogonal system (Takenaka-Malmquist system), this note gives a proof for existence of n-best rational approximation to functions in the Hardy H2(D) space by using pseudohyperbolic distance.