JournalszaaVol. 22 , No. 4DOI 10.4171/zaa/1180

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
Reconstructing an Analytic Function Using Truncated Lagrange Polynomials cover

Abstract

Let UU be the unit disc of the complex plane. We consider the problem of reconstructing a function ff in the Hardy space H2(U)H^2(U) from values f(zn(m))f(z^{(m)}_n), where {zn(m)}\{z^{(m)}_n\}, (mN(m \in {\Bbb N}; 1nm)1 \le n \le m), is a given point system in UU. This is an ill-posed problem. The function ff is approximated by so-called truncated Lagrange polynomials. Necessary and sufficient conditions for the convergence are established and a regularization result is given.