Nikolai Andreevich Lebedev and the Leningrad School of Function Theory in the 50s–70s

Abstract

Nikolai Andreevich Lebedev was born on August 8, 1919, in Krasnovochka Village, Oleninski district of Kalinin (now Tver’) oblast, in the family of a railway worker. In 1937, N. A. Lebedev was graduated from high school and became a student of Leningrad University. In 1941, Nikolai Andreevich completed the fourth year at the Faculty of Mathematics and Mechanics and entered the People’s Volunteer Corps. In July of 1941, he was sent for study to the Leningrad Airforce Academy (now the A. F. Mozhaisky University of Space Engineering). In 1944, N. A. Lebedev was graduated from the Engineering Faculty and began to teach mathematics at the Academy. In 1946, after the return of the Academy to Leningrad, N. A. completed the course at Leningrad University. Working at the Academy, Nikolai Andreevich showed himself to be an excellent teacher. He was a master of style; his lectures were strict and deep. He did a lot of scientific consulting for students and staff of the Academy. This work reflected his high level of inventiveness and his ability to solve various mathematical problems by simple and elegant methods. These qualities of N. A. Lebedev were characteristic for all of his research. Sergei Mikhailovich Lozinsky and many other Leningrad mathematicians worked at the Academy. S. M. Lozinsky was one of the first in recognizing the mathematical abilities of N. A. Lebedev. Later, S. M. Lozinsky played a large role in the life of N. A. Lebedev. On the advice of Sergei Mikhailovich, N. A. Lebedev began to participate in the seminar in geometric function theory (GFT). Gennady Mikhailovich Goluzin, the head of the seminar, was a world-renowned scientist. At the same time, Isaak Moiseevich Milin also participated in Goluzin’s seminar. The work at the seminar and personal scientific contacts with Gennady Mikhailovich determined the scientific interests of N. A. Lebedev and I. M. Milin; GTF became the main research field of their lives. From that time on, N. A. Lebedev and I. M. Milin were closed friends; their common scientific interests promoted their friendship. In the beginning of 1951, N. A. Lebedev and M. I. Milin defended their candidate’s dissertations in GTF at the Scientific Counsil of Leningrad University (G. M. Goluzin insisted that both dissertations were defended at the same day). In 1951, the dissertations were approved by the Highest Attestation Committee. In 1951, N. A. Lebedev began to teach at the Chair of Mathematical Analysis of Leningrad University (simultaneously with teaching at the Academy). From that time, Nikolai Andreevich was permanently connected with the University. After Goluzin’s death in 1952, N. A. Lebedev became the head of the seminar in GTF founded by G. M. Goluzin. In 1955, N. A. defended his doctoral dissertation; in 1957, he received the title of professor. From his demobilization in 1968 till the end of his life, N. A. Lebedev was professor of the Chair of Mathematical Analysis of Leningrad University. In his research, N. A. Lebedev developed with dignity the traditions of the St. Petersburg–Leningrad mathematical school. His results influenced the development of GFT in our country. This theory studies general classes of functions defined on simply connected domains, on multiply connected domains, or on Riemann surfaces. The peculiarity of GFT is determined by the following fact: this theory is concentrated mostly on properties of the above-mentioned classes as classes of mappings and pays less attention to analytic representations of functions from these classes. For this reason, methods of GFT are mostly geometric. Many basic problems of GFT are connected with univalent functions. N. A. Lebedev began his research at the end of the 1940s. At that time, GFT was a relatively young field. The following methods composed the list of main tools of the theory: the area method (and the method of contour integration closely connected with the area method), Lowner’s method of parametric representations (the first nonelementary method of GFT), and variational methods (methods of boundary and interior variations developed by M. Schiffer and the method of inner variations developed by G. M. Goluzin in 1946-47).