19 citations · 27 across the 10 of their papers we have counts for
7 papers · 1 filter
Steiner-Minkowski Polynomials of Convex Sets in High Dimension, and Limit Entire Functions
Victor Katsnelson
For a convex set (K) of the (n)-dimensional Euclidean space, the Steiner-Minkowski polynomial (M_K(t)) is defined as the (n)-dimensional Euclidean volume of the neighborhood of the…
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…
An Abstract Interpolation Problem and the Extension Theory of Hermitian Operators
Victor Katsnelson, Alexander Kheifets, Peter Yuditskii
The algebraic structure of V.P. Potapov's Fundamental Matrix Inequality (FMI) is discussed and its interpolation meaning is analyzed. Functional model spaces are involved. A genera…
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…