19 citations · 27 across the 10 of their papers we have counts for
6 papers · 1 filter
On H.Weyl and J.Steiner polynomials
Victor Katsnelson
The paper deals with root problems for two classes of univariate polynomials both of geometric origin. The first class discussed, the class of Steiner polynomial, consists of polyn…
On the Theory of Matrix Valued Functions Belonging to the Smirnov Class
Victor Katsnelson, Bernd Kirstein
A theory of matrix-valued functions from the matricial Smirnov class ${\goth N}_n^+({\Bbb D})$ is systematically developed. In particular, the maximum principle of V.I.Smirnov, inn…
On Transformation of Potapov's Fundamental Matrix Inequality
Victor Katsnelson
According to V.P.Potapov, a classical interpolation problem can be reformulated in terms of a so-called Fundamental Matrix Inequality (FMI). To show that every solution of the FMI…
Contributions of Issai Schur to Analysis
Harry Dym, Victor Katsnelson
The name Schur is associated with many terms and concepts that are widely used in a number of diverse fields of mathematics and engineering. This survey article focuses on Schur's…
Right and Left Joint System Representation of a Rational Matrix Function in General Position (System Representation Theory for Dummies)
Victor Katsnelson
For a rational matrix function R of one variable in general position, the matrix functions R(x)/R(y) and R(y)\R(x) of two variables are considered. For these matrix functions of tw…
Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functions II
Victor Katsnelson, Dan Volok
In this second article of the series we study holomorphic families of generic rational matrix functions parameterized by the pole and zero loci. In particular, the isoprincipal def…