BERNSHTEYN 48 



BERNSHTEYN, SERGEI NATANQVICH (Mathematician) 



S. N. Bernshteyn was born March 6, 1880 in Odessa. He did 

 graduate work in the Sorbonne in 1899 and also at the Paris 

 Higher Electrical Engineering School in 1901. In 1904 he re- 

 ceived the Doctor of Mathematical Science in Paris and in 1914 

 the Doctor of Pure Mathematics at POiarkov. From 1907 to 

 1908 Bernshteyn was professor at the Petersburg Women's 

 Poly technical School and from 1908 to 1918, professor at the 

 Higher School for Women at Kharkov. He taught at Kharkov 

 University from 1907 to 1933 and in 1920 became a professor 

 there. He was a professor at the Leningrad Polytechnical Insti- 

 tute during 1933-1941 and about the same time, 1934-1941, at 

 Leningrad University. In 1935 he joined the staff of the Mathe- 

 matics Institute of the U.S.S.R. Academy of Sciences. Bern- 

 shteyn was elected a Corresponding Member of the U.S.S.R. 

 Academy of Sciences in 1924, and in 1929 an Academician. 

 Since 1925 he has been a member of the Ukrainian Academy of 

 Sciences. He was made an Honorary Member of the Moscow 

 Mathematical Society in 1940. In 1955 he became a Foreign 

 Member of the Paris Academy of Sciences. He was awarded in 

 1941 a Stalin Prize. 



Bernshteyn' s scientific work deals chiefly with the theory of 

 differential equations, and the theory of approximations by poly- 

 nomials of functions. Early investigations (1903) of second 

 order equations of the elliptical type led him to the conclusion 

 that under certain general conditions their solutions become 

 analytical functions which can be represented as a power series. 

 Bernshteyn developed a new method of solving elliptical differ- 

 ential equations. He also studied the functional approximation of 

 polynomials, further developing the theory proposed by P. L. 

 Chebishev and continued by the scientists of the Petersburg 

 School. This work establishes the accuracy with which a 

 function can be approximated by polynomials of different powers 

 and by differential functional properties (as for instance 

 through derivatives of a definite order). Bernshteyn, with his 

 students, created a new branch in the theory of functions, which 

 he called "the constructive theory of functions." His contri- 

 butions in the field of probability are: the establishment of an 

 axiomatic structure of the theory of relativity (1917); investi- 

 gations of finite theorems (continuation and completion of the 

 work of A. A. Markov, Sr. and A. M. Lyapunov); study of sto- 

 chastic differential equations and the practical application of 

 the theory of probability to solutions of problems in physics 

 and statistics. 



