Privalov, Ivan Ivanovich
Born Jan. 30 (Feb. 11), 1891, in Nizhnii Lomov, in what is now Penza Oblast; died July 13, 1941, in Moscow. Soviet mathematician. Corresponding member of the Academy of Sciences of the USSR (1939).
Privalov graduated from Moscow University in 1913. In 1918 he became a professor at the University of Saratov; and in 1922 at Moscow University. In 1918 he published the monograph The Cauchy Integral, containing theorems both on the boundary properties of a function that conformally maps areas with rectifiable boundaries onto one another and on the boundary properties of Cauchy integrals. The main results from the theory of functions of a complex variable are set forth in the monograph Boundary Properties of Single-valued Analytic Functions (1941). In his research, Privalov systematically applied the methods of the metric theory of functions of a real variable. Privalov was also the author of works on the theory of trigonometric series and the theory of subharmonic functions, such as the monograph Subharmonic Functions (1937), and of textbooks, including Introduction to the Theory of Functions of a Complex Variable, (1927), Integral Equations (1935), and Analytic Geometry (1927).