Nevanlinna-Pick interpolation on Sobolev space

Abstract:

In this paper we shall prove an analog of the classical result of Nevanlinna and Pick concerning the bound of holomorphic functions on the unit disc that take prescribed values at prescribed points with the role that the classical Hardy space of analytic functions with square integrable power series plays in the modern operator-theoretic formulation of that result instead played by a Sobolev space of complex functions on the interval $[0,1]$ whose derivatives are in ${L^2}\left ( {0,1} \right )$.