Hardy spaces Ill-posedness of problems Truncated Lagrange polynomials Uniformly distributed point systems
Issue Date:
2003
Publisher:
Zeitschrift fur Analysis und ihre Anwendung
Citation:
Volume 22, Issue 4, Page 925-938
Abstract:
Let U be the unit disc of the complex plane. We consider the problem of reconstructing a function / in the Hardy space H2(U) from values f(zn(m)), where {zn(m)} (m ∈ ℕ 1 ≤ n ≤ 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.
