A new algorithm for meromorphic Nevanlinna-Pick interpolation

Abstract

Let D be be the open unit disc H ∞0 the space of all bounded analytic functions in D and H ∞k the set of all functions of the form f(z)/(z-z 1)...(z-z k ) where z 1...z k D and f H ∞0. Given {z 1...z n }{w 1...w n } where z i Dw i [InlineMediaObject not available: see fulltext.] and z i ≠ z j if i ≠ j we show for 0 ≤ k ≤ n-1 under certain assumptions how to construct the unique interpolating function B k H ∞k B k (z j )=w j of minimal essential supremum norm on ∂ D by solving an eigenvalue problem defined by the interpolation data. The function B k is a scaled quotient of two finite Blaschke products. © Springer-Verlag Berlin Heidelberg 2005.