Integral Equations and Operator Theory

, Volume 6, Issue 1, pp 804–840

Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions

  • Joseph A. Ball
Article

DOI: 10.1007/BF01691925

Cite this article as:
Ball, J.A. Integr equ oper theory (1983) 6: 804. doi:10.1007/BF01691925

Abstract

Classical interpolation problems are concerned with the problem of finding an analytic function on the unit disk bounded by one which takes on prescribed values at certain prescribed points inside the disk (Pick-Nevanlinna) or on the boundary of the disk (Loewner). We consider the problem for matrix-valued functions having as many as poles ( a nonnegative integer) inside the disk but still uniformly bounded by one on the boundary of the disk. Our technique is an adaptation of that of Sz.-Nagy and Koranyi to spaces with an indefinite inner product. The problem arises in the broadband matching problem for electrical circuits and certain multichannel scattering problems in physics.

Copyright information

© Birkhäuser Verlag 1983

Authors and Affiliations

  • Joseph A. Ball
    • 1
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA