Minimal Pencil Realizations of Rational Matrix Functions with Symmetries

1998 ◽  
Vol 41 (2) ◽  
pp. 178-186 ◽  
Author(s):  
Ilya Krupnik ◽  
Peter Lancaster
Keyword(s):  
Unit Circle ◽  
Real Line ◽  
Matrix Functions ◽  
Rational Matrix ◽  
The Real ◽  
Minimal Realizations

AbstractA theory of minimal realizations of rational matrix functions W(λ) in the “pencil” form W(λ) = C(λA1 − A2)−1B is developed. In particular, properties of the pencil λA1 − A2 are discussed when W(λ) is hermitian on the real line, and when W(λ) is hermitian on the unit circle.

scholarly journals New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1322
Author(s):  
Luis E. Garza ◽  
Noé Martínez ◽  
Gerardo Romero
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Linear Systems ◽  
Real Line ◽  
Stability Criteria ◽  
The Real ◽  
Discrete Linear Systems ◽  
New Criterion ◽  
Schur Stability

A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation. Some examples are presented.

Factorizations of and extensions to J-unitary rational matrix functions on the unit circle

1992 ◽  
Vol 15 (2) ◽  
pp. 262-300 ◽  
Author(s):  
I. Gohberg ◽  
M. A. Kaashoek ◽  
A. C. M. Ran
Keyword(s):  
Unit Circle ◽  
Matrix Functions ◽  
Rational Matrix

scholarly journals Rational approximants associated with measures supported on the unit circle and the real line

2011 ◽  
Vol 236 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Ruymán Cruz-Barroso ◽  
Pablo González-Vera ◽  
Francisco Perdomo-Pío
Keyword(s):  
Unit Circle ◽  
Real Line ◽  
Rational Approximants ◽  
The Real

scholarly journals Uniform point variance bounds in classical beta ensembles

2020 ◽  
pp. 2150033
Author(s):  
Joseph Najnudel ◽  
Bálint Virág
Keyword(s):  
Unit Circle ◽  
Real Line ◽  
Variance Bounds ◽  
Multiplicative Constant ◽  
The Real ◽  
Beta Ensembles ◽  
Gaussian Formula

In this paper, we give bounds on the variance of the number of points of the Circular and the Gaussian [Formula: see text] Ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized length of these sets, which is expected to be optimal up to a multiplicative constant depending only on [Formula: see text].

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