Prof. Zinchenko's research is in analysis and mathematical physics with focus on problems in approximation and spectral theory. His work in spectral theory concerns spectral properties and inverse problems for Sturm-Liouville, Schrodinger, and Jacobi operators. Zinchenko's work in approximation theory focuses on properties of extremal polynomials such as Chebyshev and orthogonal polynomials.

A list of recent publications is available on Google Scholar.