4 papers
math.CV2023
Darlington's Theorem for Rational Nevanlinna Functions in Several Variables
M. F. Bessmertnyi
Every rational Nevanlinna function in n variables is a Cayley inner function in n + 1 variables with one variable fixed in the upper half-plane.
math.CV2022
SOS Polynomials and Matrix Representations of Rational Real Functions
M. F. Bessmertnyi
The characteristic properties of Artin's denominators in Hilbert's 17th problem are obtained. It is proved that numerators of partial derivative of rational real function from the…
math.CV2021
Rational Matrix-Valued Pick Functions of Several Variables
M. F. Bessmertnyi
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
math.CV2021
Holomorphic Rational Functions of Several Variables and Sums of Squares of Polynomials
M. F. Bessmertnyi
Necessary and sufficient conditions are obtained under which the numerator of the partial derivative of a rational function holomorphic in open upper poly-halfplane is the sum of s…