Minimal Models for N∞κ-functions

Aad Dijksma, Annemarie Luger, Yuri Shondin

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Abstract

We present explicit realizations in terms of self-adjoint operators and linear relations for a non-zero scalar generalized Nevanlinna function N(z) and the function ^N(z) = −1/N(z) under the assumption that ^N(z) has exactly one generalized pole which is not of positive type namely at z = ∞. The key tool we use to obtain these models is reproducing kernel Pontryagin spaces.
Original languageEnglish
Title of host publicationEPRINTS-BOOK-TITLE
PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Number of pages38
Publication statusPublished - 2005

Keywords

  • block operator matrix
  • linear relation
  • self-adjoint operator
  • symmetric operator
  • Pontryagin spaces
  • reproducing kernel spaces
  • model
  • realization
  • generalized pole
  • generalized Nevanlinna function

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