A new algorithm for meromorphic Nevanlinna-Pick interpolation

Summary. Let D be be the open unit disc, H₀ the space of all bounded analytic functions in D and H_k the set of all functions of the form f(z)/(z–z₁)...(z–z_k) where z₁,...,z_k D and f H₀. Given {z₁,...,z_n},{w₁,...,w_n}, where z_i D,w_i and z_iz_j if ij, we show for 0kn–1, under certain assumptions, how to construct the unique interpolating function B_kH_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.Mathematics Subject Classification (2000): 65E05, 30D50, 30E05Acknowledgement We are very indebted to Professor Martin Gutknecht for pointing out the necessity of Assumption A and for providing us with a translation of A]. Also valuable discussions with Professors Olof Staffans and Göran Högnäs are acknowledged. The research of the second named author was supported by the Academy of Finland Project 51906.