Background

Ivan Ivanovich Privalov was born on January 30, 1891, the son of Ivan Andreevich Privalov, a merchant, and Eudokia Lvovna Privalova.

Education

Privalov graduated from the Gymnasium in Nizhniy Novgorod in 1909 and in the same year entered the department of physics and mathematics of Moscow University. He graduated in 1913 and remained at the university to prepare for an academic career. His scientific supervisor was D. F. Egorov, and his work was greatly influenced by N. N. Lusin. In 1916 he received his Master of Science degree.

He received his doctorate in physics and mathematics in 1935 without defending a dissertation.

Career

In 1917 Privalov became a professor at Saratov University. Privalov returned to Moscow in 1922 and for the rest of his life he was a professor of the theory of functions of a complex variable; from 1923 he also taught at the Air Force Academy.

Privalov’s first works, dealing with orthogonal series and integral equations, appeared in 1914; he then turned to the study of properties of Fourier series. His principal interests soon concentrated, however, upon boundary properties of analytic functions, that is, their properties in the vicinity of the set of their singular points; a considerable part of his seventy-nine published works is concerned with these problems. Privalov was closely preceded in this field by V. V. Golubev, another Moscow mathematician who taught at Saratov University and in 1916 published his master’s degree thesis on analytic functions with a perfect set of singular points.

In 1917 Privalov and Lusin established a wide-ranging program of studies on the theory of analytical functions by means of the theory of measure and Lebesgue integrals and began to put it into effect at once. In “Cauchy Integral” (1918), which continued the works of Pierre Fatou (1906) and Golubev (1916) and was initially intended as a master's degree thesis, Privalov described many new discoveries in the theory of boundary properties of analytic functions defined in the domain bounded by one rectifiable curve. Thus it was proved that under the conformal mapping of such domains the angles are preserved on the boundary almost everywhere.

Privalov and Lusin established the invariance of a point set with a measure equal to zero on the boundary; and Privalov solved many problems on the unicity of analytical functions, proved the existence almost everywhere of the Cauchy type of integral, established its boundary properties, and investigated in detail the problem of determining the analytical function with its values on the boundary by means of the Cauchy type of integral. Because “Cauchy Integral” appeared at a time when scientific contacts between Russia and other countries were almost nonexistent, it did not attract attention abroad.

In 1924-1925 some of the results obtained in that work were reported by Privalov in two articles in French, the second of which was written with Lusin. These results were considerably supplemented here by the solution of a number of new and difficult problems of the unicity of analytic functions determined by the set of their values on the boundary.

In 1934 Privalov began to study subharmonic functions, which had been introduced as early as 1906 and became the subject of Riesz's works in 1925-1930. In Subgarmonicheskie funktsii Privalov presented an original systematic construction of the general theory of this class of functions in close connection with the theory of harmonic functions.

He also elaborated the ideas of his work on Cauchy’s integral. Shortly before his death Privalov summarized many studies in Granichnye svoystva odnoznachnykh analiticheskikh funktsy.

Achievements

• One of the Privalov's major achievements was in presenting of original systematic construction of the general theory of subharmonic functions in close connection with the theory of harmonic functions.
  
  Also, he described many new discoveries in the theory of boundary properties of analytic functions defined in the domain bounded by one rectifiable curve in his important work “Cauchy Integral” (1918),
  
  Some of Privalov’s manuals, especially university-level courses on the theory of functions of complex variables and a manual of analytical geometry for technological colleges, became very widely used during his time in the Soviet Union.

Works

• book

  • Vvedenie v teoriju funkcij komplexnogo peremennogo./Privalov And. Introduction to the theory of functions of complex variable 1948
  • Subgarmonicheskie funkcii 1937
  • Granichnye svojstva analiticheskih funkcij 1950

Religion

Privalov stated that religious faith contradicts people’s efforts to obtain the truth about nature and a human being.

Politics

Privalov believed that Marxism–Leninism as the only truth could not, by its very nature, become outdated.

Membership

Privalov was an active member of the Moscow Mathematical Society, of which he was vice-president from 1936. He was elected a corresponding member of the Soviet Academy of Sciences in 1939. He was also a member of the French Mathematical Society (Société Mathématique de France) and the Mathematical Circle of Palermo (Circolo Matematico di Palermo).

Personality

At the end of his life, Privalov suffered from devastating emotional distress caused by a tremendous mental strain that he was going through and by the news regarding the beginning of the World War II, which resulted in his insanity.

Connections

Father:

Ivan Andreevich Privalo

Mother:

Eudokia Lvovna Privalova

collaborator:

Nikolai Nikolajewitsch Lusin

9 December 1883 – 28 January 1950, a Soviet Russia mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation and went on to apply it in other areas of mathematics.

teacher:

Dmitri Egorov

References

• Dictionary of Scientific Biography
  1975