Abstract.
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Daniel Alpay wishes to thank the Earl Katz family for endowing the chair which supported his research.
Rights and permissions
About this article
Cite this article
Alpay, D., Gohberg, I. Discrete Systems and their Characteristic Spectral Functions. MedJM 4, 1–32 (2007). https://doi.org/10.1007/s00009-007-0099-9
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00009-007-0099-9