Victor Katsnelson
The Ruth and Sylvia Shogam Professor
My field is the analysis of functions
whose values are matrices, rather than say numbers. Such functions arise in
many applications, especially signal processing and electrical engineering.
They are fundamental in the so-called spectral analysis, namely the analysis
of measured outcomes of a given signal. I am working on approximation and interpolation
problems associated with sampling such signals, and the possibility of embedding
the function that gives rise to a given sample in a manageable space. I am working
also on the analytic theory of differential equations.
Recent Publications
- [with D. Volok] Rational solutions of the Schlesinger system and isoprincipal deformations of rational matrix functions. Part 1. In: Current trends in operator theory and its applications, 291--348, Oper. Theory Adv. Appl. 149, Birkhäuser, Basel, 2004.
- [with D. Volok] Rational solutions of the Schlesinger system and isoprincipal deformations of rational matrix functions. Part II. In: Operator theory, systems theory and scattering theory: multidimensional generalizations, 165--203, Oper. Theory Adv. Appl. 157, Birkhäuser, Basel, 2005.
- [with D. Volok] Deformations of Fuchsian systems of linear differential equations and the Schlesinger system. Math. Phys. Anal. Geom. 9 (2006), no. 2, 135--186.