Our distinguished colleague, Professor Boris Levitan, died in Minneapolis on April 4, 2004. He was 89 years old. Probably his most important contribution to Mathematics is the Gelfand-Levitan equation. Gelfand and Levitan introduced this equation to study inverse scattering problems. For more details about his life, please refer to the April 14, 2004 Star Tribune obituary by Neal Gendler. This obituary also contains remarkable stories of his life, such as when he fought in the battle of Stalingrad and he was nearly shot in a strafing attack so close that he could see the pilot’s face.
He came to Minnesota at the invitation of Professor Fabes and he worked with one of our colleagues Professor Max Jodeit. Thanks to Max for contributing the reminiscences that follow.
Working with Boris Levitan
by Max Jodeit, Jr.
Sometime in the mid-nineties, Boris Levitan came to my office, then in Murphy Hall, with a question he wanted help with. I was able to deal with that question and he insisted, over my objections, that I be a coauthor. David Sattinger was still here then and he suggested a place to send it. The result was:
The isospectrality problem for the classical Sturm-Liouville equation, Max Jodeit, Jr. and B. M. Levitan, Advances in Differential Equations 2(1997)297 - 318.
One important keyword for Boris Levitan: focus! He invited me to continue with some further questions of his, and we met at the place he shared with our emeritus faculty at that time. He had to work hard to teach me the Gelfand-Levitan method!
Boris wanted to make that method work in the context of vector-valued Sturm-Liouville problems rather than the “classical,” or scalar-valued case. This led to:
A characterization of some even vector-valued Sturm-Liouville problems, Max Jodeit, Jr. and B. M. Levitan, Matematicheskaya fizika, analiz, geometriya 5(1998)166 - 181.
During our work together I learned some new phrases. Something “has place” if it holds. If an idea did not work, Boris would say “I am destroyed!” These came up often in the next phase, the vector-valued analog of the first paper. The work was announced in a note in 1998:
Isospectral Vector-Valued Sturm-Liouville Problems, Max Jodeit, Jr. and B. M. Levitan, Letters in Mathematical Physics 43 (1998)117 -122.
The last paper we worked on took some time and much effort.
The Isospectrality Problem for Some Vector-Valued and B. M. Levitan, Russian Journal of Mathematical Physics 6 (1999)375 - 393.
Though Boris had many other ideas and problems, his health kept him from his mathematical life. I remain glad to have known him and grateful that I actually had the chance to work with him.
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