About the Rationality of the Knizhnik-Zamolodchikov Equation Solution (2009)
In the paper the solution of KZ system (n=4, m=2) is constructed in the explicit form in terms of the hypergeometric functions. We proved that the corresponding solution is rational when the...
Infinite Hankel Block Matrices, Extremal Problems (2009)
In this paper we use the matrix analogue of eigenvalue $\rho_{min}^{2}$ to formulate and to solve the extremal Nehary problem. When $\rho_{min}$ is a scalar, our approach coincides with...
MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL SYSTEMS, PAINLEVÉ TYPE FUNCTIONS (2008)
Lev Sakhnovich, E. A. Coddington, N. Levinson, Theory Ordinary, Differential Equations, Mcgraw-hill Book
O perators a nd M atrices
On the solutions of Knizhnik-Zamolodchikov system (2008)
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of KZ system...
Open Problems On, Vincent D. Blondel, Alexander Megretski, Roger Brockett, Jean-michel Coron, Miroslav Krstic, ...
this paper we consider the well-known Schur problem the solution of which satisfy in addition the extremal condition (z)w(z) min ; jzj < 1 (58.1) where w(z) and min are mxm matrices and min > 0...
Explicit Rational Solutions of Knizhnik-Zamolodchikov Equation (2007)
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group $S_{n}$. We assume...
Rational solutions of KZ equation, case $S_4$ (2007)
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are generated by elements of the symmetric group $S_n$. We separately investigate the...
Integral Equations in the Theory of Levy Processes (2007)
In this article we consider the Levy processes and the corresponding semigroup. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory...
Rational solutions of Knizhnik-Zamolodchikov system (2006)
We consider Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of KZ system is...
Meromorphic Solutions of Linear Differential Systems, Painleve type functions (2006)
We consider the $n{\times}n$ matrix linear differential systems in the complex plane. We find necessary and sufficient conditions under which these systems have meromorphic fundamental solutions....
On Sample Functions Behavior of Stable Processes (2006)
We investigate the asymptotic behavior of sample functions of stable processes when $t{\to}\infty$. We compare our results with the iterated logarithm law, results for the first hitting time and most...
Vadim Olshevsky, Lev Sakhnovich
Abstract. The classical Kharitonov theorem on interval stability cannot be carried over from polynomials to arbitrary entire functions. In this paper we identify a class of entire functions for which...
Integrable Operators and Canonical Differential Systems (2004)
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem,...
Vincent D. Blondel, Alexander Megretski, Roger Brockett, Jean-michel Coron, Miroslav Krstic, Anders Rantzer, ...
Some of the problems appearing in this booklet will appear in a more extensive forthcoming book on open problems in systems theory. For more information about this future book, please consult the...