Discrete systems and their characteristic spectral functions

Daniel Alpay, Israel Gohberg

Research output: Contribution to journalArticlepeer-review


We define first-order discrete systems in the matrix-valued case. They are characterized by sequences of pair of matrices, called admissible sequences. We present two important examples of such sequences, called Szegö and Nehari sequences. We introduce the characteristic spectral functions associated to a first-order system. We define in particular the scattering function, the Weyl function and the reflection coefficient function and we study the relationships between these functions.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalMediterranean Journal of Mathematics
Issue number1
StatePublished - 1 Apr 2007


  • Discrete systems
  • Scattering matrix
  • State space method

ASJC Scopus subject areas

  • Mathematics (all)


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