# Reconstructing an Analytic Function Using Truncated Lagrange Polynomials

### Dang Duc Trong

National University, Hochiminh City, Vietnam### Tran Ngoc Lien

Faculty of Natural Sciences, Cantho City, Vietnam

## Abstract

Let $U$ be the unit disc of the complex plane. We consider the problem of reconstructing a function $f$ in the Hardy space $H^2(U)$ from values $f(z^{(m)}_n)$, where $\{z^{(m)}_n\}$, $(m \in {\Bbb N}$; $1 \le n \le m)$, is a given point system in $U$. This is an ill-posed problem. The function $f$ is approximated by so-called truncated Lagrange polynomials. Necessary and sufficient conditions for the convergence are established and a regularization result is given.