Kergin Approximation in Banach Spaces

TL;DR

This paper investigates the convergence properties of Kergin interpolation polynomials for holomorphic functions in Banach spaces, including cases of divergence, expanding understanding of approximation methods in infinite-dimensional analysis.

Contribution

It provides new insights into the convergence and divergence behavior of Kergin interpolation in Banach spaces, especially for functions not of bounded type.

Findings

Kergin interpolation can converge for certain holomorphic functions in Banach spaces.

Divergence of Kergin series is possible in some cases.

The paper characterizes conditions affecting convergence and divergence.

Abstract

We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.