Vladimir Andreevich Steklov

Born Dec. 28, 1863 (Jan. 9, 1864), in Nizhny Novgorod, now Gorky; died May 30, 1926, in the Crimea (buried in Leningrad). Soviet mathematician. Academician of the St. Petersburg Academy of Sciences (1912; corresponding member, 1902). Vice-president of the Academy of Sciences of the USSR (1919–26).

In 1887, Steklov graduated from the University of Kharkov, where he had studied under A. M. Liapunov. From 1889 to 1906, Steklov was affiliated with the chair of mechanics of the University of Kharkov; after working as an assistant, he became a pri-vatdocent in 1891 and a professor in 1896. From 1893 to 1905 he also taught theoretical mechanics at the Kharkov Institute of Technology. Steklov defended his master’s thesis, On the Motion of a Solid in a Fluid (published 1893), in 1894 and his doctoral dissertation, General Methods for the Solution of Fundamental Problems of Mathematical Physics (published 1901), in 1902. He joined the University of St. Petersburg in 1906.

Steklov was active in public life and scientific organizations, particularly in the last years of his life. In 1921 the Physicomathe-matical Institute was established on his initiative under the Academy of Sciences, and he served as its director until his death. The institute was named in honor of Steklov in 1926. It was divided in 1934 into two institutes, one of which—the Institute of Mathematics of the Academy of Sciences of the USSR—continues to bear his name.

Steklov’s scientific work centered on the application of ma-themical methods to problems in science, mainly mathematical physics. He obtained a number of important results on the fundamental problems of potential theory. He derived a Poincaré-type inequality with exact constant for functions that vanish at the boundary of a domain. Most of Steklov’s works involved series expansions of functions relative to preassigned orthogonal systems of functions; boundary value problems of mathematical physics are usually reduced to such systems. This research was based on the concept of the completeness of a system of orthogonal functions, a concept that Steklov introduced. He almost arrived at the concept of a Hubert space. In his research on series expansions, Steklov developed a number of asymptotic methods, one of which, called the Liouville-Steklov method, can be used to obtain asymptotic expressions for classical orthogonal polynomials. Steklov’s theorems on generalized Fourier expansions are quite similar to equiconvergence theorems. He introduced a special smoothing method for functions that has since been extensively developed.

Steklov was the author of several works on mathematical analysis (dealing, in particular, with the theory of quadrature formulas), on elasticity theory, and on hydromechanics. He is also known as a historian of mathematics and as a philosopher and writer. He was the author of scientific biographies of M. V. Lo-monosov and Galileo; essays and articles on the life and work of P. L. Chebyshev, N. I. Lobachevskii, M. V. Ostrogradskii, A. M. Liapunov, A. A. Markov, J. H. Poincaré, and J. Thomson; a philosophical study entitled Mathematics and Its Importance to Mankind (1923); and the book To America and Back: Impressions (1925).