The Extremal Functions Of Analytic Hilbert Spaces Over The Unit Disk

This paper deals mainly with the extremal functions in the Hilbert space X which is composed of analytic functions over the unit disk.First,we give the completing description of the zero basis subspaces in X.And then,we study the basic properties of the extremal functions and give the computational methods of the finite zero extremal functions.At last,we prove that if A={λ₁,λ₂,...,λ_n...} is a subsequence of zerosequence in X,G_n is the extremal function corresponding the A_n={λ₁,λ₂,...,λ_n}, then the extremal function ofΛis the norm limit of G_n.