PEOPLE OF SOVIET SCIENCE

VLADIMIR IVANOVICH SMIRNOV

(On the 80th anniversary of his birth)

On June 10, 1967, 80 years had passed since the birth of the outstanding Soviet mathematician, educator, historian, and organizer of science, the State Prize laureate Academician Vladimir Ivanovich Smirnov.

V. I. Smirnov was born in Petersburg. In 1910 he graduated from Petersburg University and, beginning in January 1912, was retained at the university to prepare for the rank of professor—in modern terminology, he was kept on as a postgraduate student—and from 1915 he taught at the same university. In 1918 Vladimir Ivanovich defended his master’s dissertation, and from 1926 he was a professor at Leningrad University.

For outstanding services in the field of mathematics, V. I. Smirnov was elected a corresponding member in 1932, and in 1943 a full member of the Academy of Sciences of the USSR. In 1948, for his fundamental Course of Higher Mathematics, he was awarded the State Prize.

For many years of work at Leningrad University, Vladimir Ivanovich headed several departments: mathematical analysis, the theory of functions of a complex variable, the theory of elasticity, hydroaeromechanics, and others; from 1931 to 1937 he was deputy director of the Scientific Research Institute of Mathematics and Mechanics of Leningrad State University, and later (1937–1952) director of that institute.

From 1928 to 1934 he worked at the Seismological Institute of the Academy of Sciences of the USSR, heading the theoretical department of that institute.

At present V. I. Smirnov heads the department of mathematics in the faculty of physics and the department of mathematical physics in the faculty of mathematics and mechanics of Leningrad University.

The range of V. I. Smirnov’s scientific interests is very broad, and his mathematical talent is extraordinarily many-sided. In his first major work, published in 1918, Vladimir Ivanovich studies the problem of uniformization for an irreducible algebraic equation \(f(x, y)=0\) and gives a very simple and elegant solution of it by means of Fuchsian functions, single-valued and regular in the unit disk and having the circumference of this disk as their natural boundary.

In his works of 1918–1921 V. I. Smirnov studies in detail the problems of inversion of a linear differential equation of the second order with four singular points. In particular, he gives a complete picture of the spectrum of such an equation and determines under what conditions the inversion problem has a unique solution.

In the field of the analytic theory of differential equations V. I. Smirnov worked up to and including 1927, until the publication of his work “On the fundamental domain of the groups of motions on the Lobachevsky–Bolyai plane.”

In the second half of the 1920s, under the guidance of V. I. Smirnov, I. A. Lappo-Danilevsky began working in the field of the analytic theory of differential equations. The methods of investigation created by this remarkable scholar, based on the broad application of the theory of analytic functions of matrices, completely changed the face of the analytic theory of systems of linear differential equations.

Lappo-Danilevsky’s investigations were successfully continued by other students of V. I. Smirnov—Academician N. E. Kochin and Academician of the Academy of Sciences of the Byelorussian SSR N. P. Erugin; the latter, in particular, solved the well-known Poincaré problem.

At the end of the 1920s V. I. Smirnov’s scientific interests shifted from the analytic theory of differential equations to boundary questions in the theory of functions of real and complex variables. He took up questions of expanding regular functions in series of polynomials orthogonal on the contour of a domain. In particular, in 1928 he established a certain important class of domains with rectifiable boundary (now called the class \(C\)), for which expansion in a series of polynomials orthogonal on the boundary holds for all functions regular in the domain and whose boundary values (in a certain, precisely defined sense) are integrable with their square over the boundary of the domain. In the case of an analytic boundary, expansion theorems are also obtained for functions merely regular in the domain. However, in this case the expansion is not a Fourier series for the function.

In 1928–1933 V. I. Smirnov investigated in detail the principal apparatus for representing functions of a complex variable—the Cauchy and Green integrals and various parametric representations. He also studied various classes of functions that arise naturally in such a consideration. In particular, he substantially supplemented the theorem on the maximum modulus of a regular function. In addition, V. I. Smirnov investigated the correspondence of boundaries under conformal mapping. All these fundamental investigations constitute a new chapter in our knowledge in the field of the theory of functions.

V. I. Smirnov’s works on related questions in the theory of functions of real and complex variables attracted the attention of a number of outstanding scholars. Thus, Academicians M. V. Keldysh and M. A. Lavrentiev showed (in 1937) that the class \(C\) is narrower than the entire class of domains with rectifiable boundary.

V. I. Smirnov drew the attention of G. M. Goluzin to questions of the geometric theory of functions of a complex variable. This outstanding scholar is responsible for a whole series of fundamental results in the geometric theory of functions.

Over a number of years Vladimir Ivanovich worked extensively and fruitfully on various questions of the constructive theory of functions of a complex variable, and quite recently, together with his student N. A. Lebedev, published a fundamental work on

this set of problems—“A Constructive Theory of Functions of a Complex Variable.”

In the 1930s V. I. Smirnov carried out (partly together with his pupil S. L. Sobolev) a number of very interesting and important works on the theory of wave propagation. In these works the apparatus of the theory of functions of a complex variable was applied with great success to the solution of partial differential equations. The method of investigation used here is based on the construction of so-called functionally invariant solutions of the wave equation.

Very interesting are V. I. Smirnov’s works on the theory of elasticity, belonging to the same period, in which the new method of incomplete separation of variables, created by the author, is remarkable. In these works a new chapter of mathematical physics and, at the same time, an important branch of theoretical seismology arose—the theory of vibrations of layered media. Later (1952–1954) V. I. Smirnov successfully applied the same methods to problems of geometry (the theory of isotropic congruences).

Vladimir Ivanovich devoted, and continues to devote, much time and effort to questions of teaching mathematics in higher education. He created the fundamental five-volume Course of Higher Mathematics. This work—the only encyclopedia of mathematical analysis of its kind—is distinguished by the richness of its material, the large number of applications, and the rigor and mastery of its exposition. The Course of Higher Mathematics has been translated into many languages.

It is difficult to overestimate the role of V. I. Smirnov as an organizer of scientific research in mathematics. Over many years he organized and directed a whole series of seminars on the most diverse branches of mathematical analysis. A whole number of scientific directions and even schools appeared in Leningrad thanks to the efforts of Vladimir Ivanovich. Very many mathematicians, both Leningrad and non-Leningrad, are pupils of V. I. Smirnov.

Vladimir Ivanovich, as a publisher of the scientific legacy of outstanding mathematicians and as a historian of mathematics, in our opinion has no equal.

V. I. Smirnov, together with N. E. Kochin, prepared from the manuscripts of I. A. Lappo-Danilevsky and published three volumes of his works. He published A. M. Lyapunov’s widely known work “Sur certaines série de Liqures d’équilibre d’un liquide héticogine en rotation”. Largely thanks to the efforts of V. I. Smirnov, another extensive work of A. M. Lyapunov, “Investigation of One of the Special Cases of the Problem of Stability of Motion,” also saw the light of day. He also took a very active part in preparing for publication the collected works of A. M. Lyapunov and published the works of M. V. Ostrogradsky.

The numerous and interesting works of V. I. Smirnov on the history of mathematics (analysis of the correspondence of A. M. Lyapunov with H. Poincaré, J. Hadamard, and other foreign mathematicians, analysis of the works of D. Bernoulli, Euler’s correspondence, a survey of the works of A. M. Lyapunov, and others) arose as the result of investigations of archival materials. Vladimir Ivanovich is still chairman of the Council of the Archive of the Academy of Sciences of the USSR.

The unusual combination in the person of Vladimir Ivanovich of a scholar-researcher and a scholar-historian lends special interest to his publications on the history of mathematics.

The scientific and public activity of Vladimir Ivanovich is not limited to his constant, selfless participation in the affairs of Leningrad University. At the end of the 1920s he took an active part in the work of the Physico-Mathematical Society, and in the most recent period before

with the closing of the Society (1930), he was its chairman. Vladimir Ivanovich was the chief organizer of the 2nd All-Union Congress of Mathematicians (1934) and editor of the Congress Proceedings. In 1951 he organized the Leningrad City Mathematical Seminar and was its permanent chairman until 1958, when, again as a result of his efforts, this seminar was transformed into the Leningrad Mathematical Society. It is not surprising that the Leningrad Mathematical Society, which owed its origin to V. I. Smirnov, elected him its honorary president.

S. M. Lozinskii, V. A. Pliss

LITERATURE ON V. I. SMIRNOV

(only articles of a general nature are indicated,
and not reviews of books and works by V. I. Smirnov)

1. Gonze D. M. The Mathematical Institute named after V. A. Steklov. Vestn. AN SSSR, 1937, No. 10—11, pp. 32—33.

2. Full members of the Academy of Sciences of the USSR elected by the General Assembly of the Academy of Sciences of the USSR on 27 and 29 September 1943. V. I. Smirnov. Vestn. AN SSSR, 1943, No. 11—12, p. 91.

3. Awarding of the Order of the Red Banner of Labor. Vestn. AN SSSR, 1944, No. 3, p. 6.

4. Awarding of the Order of the Red Banner of Labor. Vestn. AN SSSR, 1945, No. 5—6, supplement; Izvestiya, 1945, 15/VI, No. 139.

5. Awarding of the Order of Lenin. Pravda, 1947, 31/V, No. 136.

6. Sobolev S. L. Vladimir Ivanovich Smirnov. UMN, 1947, 2, issue 6, pp. 238—239, portrait.

7. Sobolev S. L. and Fikhtengolts G. M. Academician V. I. Smirnov. Vestn. LGU, 1947, No. 6, pp. 155—157.

8. Erugin N. P. Laureate of the Stalin Prize 1948, Academician Vladimir Ivanovich Smirnov. Vestn. LGU, 1948, No. 9, pp. 122—123, portrait.

9. Awarding of the Stalin Prize. Pravda, 1948, 30/V, No. 151; Izvestiya, 1948, 30/V, No. 127.

10. Sobolev S. L. Vladimir Ivanovich Smirnov. Publishing House of the Academy of Sciences of the USSR, 1949, 44 pp., portrait.

11. Ladyzhenskaya O. A. and Fikhtengolts G. M. Vladimir Ivanovich Smirnov (on his seventieth birthday). Vestn. LGU, 1957, No. 7, pp. 5—14, portrait.

12. Aleksandrov P. S., Vekua I. N., Keldysh M. V., Lavrent’ev M. A. Vladimir Ivanovich Smirnov. UMN, 1957, XII, No. 6(78), pp. 197—206, portrait.

13. Radovskii M. I. Vladimir Ivanovich Smirnov. UMN, 1962, XVII, No. 6(108), pp. 185—190, portrait.