Discrete Systems and their Characteristic Spectral Functions

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 Szeg? 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. Daniel Alpay wishes to thank the Earl Katz family for endowing the chair which supported his research.