Boris Levitan
Boris Moissejewitsch Levitan (Russian Борис Моисеевич Левитан, English transcription Boris Levitan, born June 7, 1914 in Berdyansk, † April 4, 2004 in Minneapolis ) was a Russian or Ukrainian mathematician, known for his contributions to the theory of almost periodic functions and storm Liouville theory and particularly the theory of Inverse Problems ( Gelfand - Levitan theory ).
Life and work
Boris Levitan was born in 1914 in Berdyansk and grew up in Kharkov, where he in 1938 with the theme Some generalizations of almost periodic functions with Naum Ilyich Achijeser doctorate and habilitation in 1940 (Russian PhD ) with the labor theory of generalized translation operators. After military service from 1941 to 1944 during the Second World War, in which he was involved, among others, at the Battle of Stalingrad, he taught from 1944 to 1961 at the Felix Dschersinski Military Academy and from 1961 at the Moscow State University. Most recently, he worked at the University of Minnesota.
He was awarded the Order of Lenin.
He is best known for the Gelfand - Levitan theory with Israel Gelfand from 1951. Theory solves the problem of inverse scattering theory with (initially one-dimensional ) Sturm-Liouville problems, such as the time-independent Schrödinger equation or the wave equation with a scattering potential, ie the reconstruction of the potential from the scattering data via an integral equation ( Gelfand - Levitan equation). This was later important in soliton theory. The Gelfand - Levitan theory has been extended in Russia of Vladimir Aleksandrovich Marchenko, so that it is also called Gelfand - Levitan - Marchenko theory.
Writings
- Levitan, B. M.; Zhikov, VV: Almost periodic functions and differential equations. Cambridge University Press, Cambridge, New York, 1982. ISBN 0-521-24407-2
- Levitan, B. M.: Inverse Sturm-Liouville problems. VNU Science Press, Utrecht 1987. ISBN 90-6764-055-7
- Levitan, B. M.; Sargsyan, IS: Sturm-Liouville and Dirac operators. Kluwer Academic Publishers Group, Dordrecht, 1991. ISBN 0-7923-0992-8
- Levitan, B. M.; Sargsyan, IS: Introduction to spectral theory: selfadjoint ordinary differential operators. American Mathematical Society, Providence, RI, 1975.
- Levitan, B. M.; Gasymov, MG: Determination of a differential equation by two of its spectra, Russian Mathematical Surveys, Volume 19, 1964, p 1-63