Soon after Natanson had graduated from the University, he made his first research concerning singular integrals. Later he returned repeatedly to this subject. In the 30s S.N.Bernstein worked at the Leningrad University. Under his influence, Natanson began to work in the constructive theory of functions. In this field he worked all his life and proved himself a very strong mathematician. His research concerned series in orthogonal polynomials, interpolation processes, the moment problem, Gibbs phenomenon and other problems of the approximation theory. He also worked in "pure" theory of functions and functional analysis.

Natanson is known in broad mathematical circles as the author of a number of brilliant monographs and handbooks. His "Theory of functions of real variables" which ran into several editions in six languages is a handbook for several generations of mathematicians. In this book Natanson showed the principal trait of his pedagogical talent, a rare ability to make difficult arguments clear. "Theory of functions" is the only book in Russian where one can find proofs of such difficult theorems as Hausdorf's theorem on the sphere partition. The proofs are complete and at the same time as simple as possible. Another outstanding book by Natanson is "Constructive theory of functions". It requires only minimal mathematical background, but by the end of reading it the reader is able to participate in a scientific seminar. This comparatively small book was an introduction to mathematics for many first-rate mathematicians.

Natanson was a brilliant lecturer. He gave at the University very different courses - on integral equations, the theory of functions, the approximation theory and, of course, mathematical analysis. He disliked any sort of improvisation and polished his courses with extraordinary care. He had not equal in finding proper words. His lectures were detailed, clearly structured and at the same time laconic. The words once found by Natanson became recognized mathematical terms.

Natanson had many pupils. The contemporary Leningrad school of the constructive theory of functions consists to a great extent from his pupils. Among those who once attended his lectures are Academy of Science member E.I.Shemjakin, chair heads professors V.V.Petrov, V.A.Pliss and many other outstanding mathematicians. Natanson headed theChair of Mathematical analysis. Everybody at the Department liked him: friends, collegues, students. He was respected not only as an outstanding teacher and researcher, but also as a tactful, friendly person and a man of principle who was always guided by the sense of duty.

Reminiscences by B.M.Makarov (in Russian)

Reminiscences by V.A.Zalgaller (in Russian)

*Last updated: 12.10.03*