The Moshe Porath Professor of Mathematics
My area of research is analysis and differential equations. I am trying to infer from the local structure of ordinary and partial differential equations, the global structure of solutions. One direction of the research is to use the local algebraic properties of the coefficients of the ordinary differential equation to impose global restrictions (periodicity, stability) on the motion, defined by this equation. Another direction of my research is to use the local structure, together with a novel matching procedure, in order to compute approximate solutions. The method has to do with the examination of how complex some mathematical terms are. A similar approach helps in devising methods for image compression.
- [with M. Blinov and N. Roytvarf] Center and Moment conditions for Abel equation with rational coefficients. Funct. Diff. Equations 10 (1-2) (2003) 95-106.
- Center Problem for Abel Equation, Compositions of Functions and Moment Conditions, with the Addendum by F. Pakovich, "Polynomial Moment Problem", to appear in a special volume of the MMJ, dedicated to the 65 birthday of V.I. Arnold, 2004.
- [with M. Briskin] Tangential Hilbert problem for Abel equation, to appear, 2004.