Two classical interpolation
theorems, due to Carathéodory-Fejér and Nevanlinna-Pick, deal with classes of
functions analytic in th unit disk which take certain prescribed values at finitely
many points there. The theorems express certain extrema of these classes as
eigenvalues of finite matrices. In this paper, there is given a generalization of
this type of interpolation, which involves inner functions. It is seen that a
certain theorem about Hankel matrices and projections of Toeplitz matrices
generalizes both of the above interpolation theorems. The theorem also provides a
generalization of some recent work of the author on meromorphic interpolation and
a continuous analogue of a theorem on Toeplitz forms and interpolation.
Finally, the theorem has some consequences in the theory of infinite Hankel
matrices.
