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Vladimir Aleksandrovich Marchenko

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7 July 1922

Kharkov, Ukraine

Vladimir Marchenko attended Kharkov University, graduating in 1945. He was appointed onto the staff after graduating and worked at Kharkov University until 1961. Half way through this period, in 1953, he was promoted to professor.

In 1961 Marchenko was appointed to the Physical-Technical Institute of Low Temperature in Kharkov.

In the 1950s Marchenko obtained important results in approximation theory. His results concern the approximation theory of almost periodic functions. Also in the 1950s he studied the asymptotic behaviour of the spectral measure and of the spectral function for the Sturm - Liouville equation. In this work is described:

He is well known for his original results in the spectral theory of differential equations , including the discovery of new methods for the study of the asymptotic behaviour of spectral functions and the convergence expansions in terms of eigenfunctions . He also obtained fundamental results in the theory of inverse problems in spectral analysis for the Sturm - Liouville and more general equations.

In fact Marchenko later applied his methods to the Schrödinger equation.

The periodic case of the Korteweg -de Vries equation was solved by Marchenko in 1972. He used the method of the inverse problem in the theory of dissipation.

Petryshyn in describes other work of Marchenko including his work on self adjoint differential operators:

Marchenko made significant contributions to the theory of self-adjoint differential operators with infinitely many independent variables and also to the theory of spaces of functions of infinitely many variables as inductive limits of locally convex function spaces.

Source:School of Mathematics and Statistics University of St Andrews, Scotland