Schur-Nevanlinna sequences of rational functions

Adhemar Bultheel Andreas Lasarow

Abstract: We study certain sequences of rational functions with poles outside the unit circle. Such kind of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur-Nevanlinna algorithm for Schur functions on the one hand and on the other hand to orthogonal rational functions on the unit circle. We shall see that rational functions belonging to a Schur-Nevanlinna sequence can be used to parameterize the set of all solutions of an interpolation problem of Nevanlinna-Pick type for Schur functions.

Status:
Published

BiBTeX entry:

   @article{ArtBL04,
      author = "A. Bultheel and A. Lasarow",
      title = "Schur-{N}evanlinna sequences of rational functions",
      journal = "Proceedings of the Edinburgh Mathematical Society",
      year = "2007",
      pages = "571-596",
      volume = "50",
      number = "3",
      url = "http://nalag.cs.kuleuven.be/papers/ade/mnp/index.html",
      DOI = "10.1017/S0013091504001063",
      LIRIAS = "146690",
      ZBL = "05233231",
      MR = "2360517",
   }

File(s): preprint.pdf (269K)

Contact: Adhemar Bultheel