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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 4, 2003, pp. 925–938
DOI: 10.4171/ZAA/1180

Published online: 2003-12-31

Reconstructing an Analytic Function Using Truncated Lagrange Polynomials

Dang Duc Trong[1] and Tran Ngoc Lien[2]

(1) National University, Hochiminh City, Vietnam
(2) Faculty of Natural Sciences, Cantho City, Vietnam

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.

Keywords: Hardy spaces, truncated Lagrange polynomials, ill-posedness of problems, uniformly distributed point systems

Trong Dang Duc, Lien Tran Ngoc: Reconstructing an Analytic Function Using Truncated Lagrange Polynomials. Z. Anal. Anwend. 22 (2003), 925-938. doi: 10.4171/ZAA/1180