TY  - JOUR
ID  - Alpay2016
LB  - Alpay2016
AU  - Alpay, Daniel
AU  - Jorgensen, Palle
AU  - Lewkowicz, Izchak
TI  - Characterizations of rectangular (para)-unitary rational functions
ST  - Characterizations of rectangular (para)-unitary rational functions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 6
SP  - 695
EP  - 716
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.6.695
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.6.695
AB  - We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) through the realization matrix of Schur stable systems, (ii) the Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters, (iii) through the (not necessarily reducible) Matrix Fraction Description (MFD). In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and infinity). A special attention is devoted to exploring the gap between the square and rectangular cases.
KW  - isometry
KW  - coisometry
KW  - lossless
KW  - all-pass
KW  - realization
KW  - gramians
KW  - matrix fraction description
KW  - Blaschke-Potapov product
SN  - 1232-9274
ER  -