Discrete systems and their characteristic spectral functions

Daniel Alpay; Israel Gohberg

doi:10.1007/s00009-007-0099-9

Discrete systems and their characteristic spectral functions

Daniel Alpay, Israel Gohberg

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-32
Number of pages	32
Journal	Mediterranean Journal of Mathematics
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/s00009-007-0099-9
State	Published - 1 Apr 2007

Keywords

Discrete systems
Scattering matrix
State space method

ASJC Scopus subject areas

Mathematics (all)

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10.1007/s00009-007-0099-9

Cite this

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AB - 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.

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KW - Scattering matrix

KW - State space method

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Discrete systems and their characteristic spectral functions

Abstract

Keywords

ASJC Scopus subject areas

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