Privalov, Ivan Ivanovich

Ivan Ivanovich Privalov was born on January 30 ( February 11 ), 1891 in the city of Nizhny Lomov, Nizhnelomovsky district of the Penza province (now in the Penza region ) ^[3] , in the family of the 2nd guild merchant Ivan Andreevich Privalov and his wife Evdokia Lvovna, nee Pastushkova ( in total there were eight children in the family: sons Ivan, Andrey, Alexei, Leonid and daughters Nadezhda, Alexandra, Maria, Valentina) ^[4] . After graduating with a gold medal from the Nizhny Novgorod Gymnasium ^[5] in 1909 he entered Moscow University , where he graduated in 1913 . During his studies in the summer of 1911, he attended lectures by David Hilbert , Edmund Landau, and Felix Klein in Göttingen . D.F. Egorov was very impressed with Privalov's abilities and recommended that he stay at the university for research.

In 1915 he became vice president of the Moscow Mathematical Society .

Since 1918, in connection with the opening of new faculties in the University of Saratov, on the recommendation of Yegorov, he began to teach analytical geometry and higher algebra in Saratov ^[6] . In the same year he was awarded the title of professor . In 1921, Privalov returned to Moscow, and since 1922 he became a professor at Moscow University ^[3] .

Since 1923, he was the head of the function theory department of the Research Institute of Mathematics and Mechanics and professor at the N.E. Zhukovsky Air Fleet Academy with the rank of 1st rank military engineer, which allowed him to appear in lectures and at the university in the form of a colonel of the Air Force ^[7] .

The first major work of I. I. Privalov, “The Integral of Cauchy” ^[8] , was published in 1918. This work, which was published during the Civil War and the blockade of the RSFSR by foreign states, remained unknown for a long time abroad, and some of the results of Privalov were partially obtained by foreign scientists ( F. Rhys and others). Therefore, in 1924-1925 he returned to this topic in two French publications, one of which was written jointly with N. N. Luzin . In the future, Privalov writes a number of scientific monographs: “Subharmonic functions” ^[9] (1937) and “Boundary properties of unique analytic functions” ^[10] (1941) ^[11] .

In 1930-1931, I. I. Privalov served as the head of the department of the theory of functions of the real and complex variable physical and mechanical faculty of Moscow State University ^[12] . In 1938-1941, he headed the Department of Function Theory of the Mechanics and Mathematics Faculty of Moscow State University (formed as a result of dividing the Department of Analysis and Function Theory into two: the Department of Mathematical Analysis and the Department of Function Theory) ^{[13] [14]} .

Since 1935, I. I. Privalov is a doctor of physical and mathematical sciences ^[12] . January 29, 1939 I. I. Privalov was elected a corresponding member of the USSR Academy of Sciences in the Department of Mathematical and Natural Sciences (mathematics) ^[15] .

I. I. Privalov put a lot of energy and energy into teaching mathematics in higher education and was a brilliant lecturer who enthusiastically presented lecture material and skillfully introduced his students to the modern state of science. He created a number of first-class textbooks for universities (“Introduction to the Theory of Functions of a Complex Variable” ^[16] , “Fourier Series” ^[17] , “Integral Equations”) and for a technical school (“Analytical Geometry”, which has passed 12 editions from 1927 to 1939) ^[18] . The 30th edition of Analytical Geometry was published in 1966, twenty-five years after the death of the author; 31st - in 1991. Privalov’s textbook on the theory of functions of a complex variable (the already mentioned “Introduction to the theory of functions of a complex variable”, 1927) is considered classical; in 1999, its 14th edition was published.

However, he had almost no students. P.S. Aleksandrov explained this by the fact that Privalov knew too much and therefore demanded too much from his students.

I. Privalov combined his scientific and pedagogical activity with extensive public work: in recent years, he has been vice-president of the Mathematical Society , a member of the Higher Attestation Commission in the All-Union Committee for Higher School Affairs, and a deputy in the Krasnopresnensky District Council. For outstanding scientific and public services, I. I. Privalov in 1940 , in connection with the anniversary of Moscow University, was awarded the Order of the Red Banner of Labor ^[19] .

As a result of enormous mental stress and severe mental trauma caused by the catastrophic start of the Great Patriotic War for the USSR, Privalov went crazy. Ivan Ivanovich Privalov died on July 13, 1941 in Moscow ^[15] .

The main directions of scientific research of I. I. Privalov related to the theory of functions of a complex variable , the theory of trigonometric series , the theory of functions of a real variable ^[3] .

In his monograph “The Cauchy Integral” ^[8] (1918), Privalov presented a number of important results he obtained: theorems on the boundary properties of functions conformally mapping onto each other domains with rectifiable boundaries, boundary properties of integrals of the Cauchy type, etc. ^[3] In a joint article by I. I. Privalov and N. N. Luzin in 1924 ^[20] , the Luzin – Privalov theorem on the invariance of boundary points of measure zero under a conformal mapping of the circle was proved {\ displaystyle | z | <1}   to the area${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">D</span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">,</span></span>}$ {\ displaystyle D,}   which takes place if the boundary${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">L</span></span>}}$ {\ displaystyle L}   areas of${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">D</span></span>}}$ {\ displaystyle D}   - rectifiable closed curve of Jordan ^[21] . In another joint article ^[22] , published a year later, a uniqueness theorem was established for holomorphic functions : if a function is holomorphic in the unit disk${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">f</span></span>}}$ {\ displaystyle f}   has angular limit values (or radial limit values ) on the set of points of the unit circle of positive measure, then with these values ​​the function${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">f</span></span>}}$ {\ displaystyle f}   defined uniquely. In 1938 ^[23] Privalov extended this result to meromorphic functions ^[24] .

II Privalov is credited with the systematic development of the general theory of subharmonic functions and its various applications to the theory of analytic functions (in particular, to problems of studying the boundary properties of analytic functions). He carried out this development in a large cycle of works starting in 1934 ^{[18] [25]} .

From the results of I. I. Privalov, which are not related to the theory of analytic functions , it should be noted that he made a major contribution to the study of the properties of conjugate Fourier series concerning the convergence of the conjugate series and its differential properties ^[18] .

In Nizhny Lomovo, the house of merchant Ivan Avksentievich Lopatin was preserved, where the Privalov family lived for some time. It is marked with a plaque in memory of the fact that I. I. Privalov was born here ^[4] .

Selected Editions

• Privalov I. I. Introduction to the theory of functions of a complex variable: A manual for higher education. - M .; L .: State Publishing House, 1927. - 316 p.
• Privalov I.I. Fourier series. - 3rd ed., Reprint. without changes from the 2nd ed. - M .; L .: ONTI: State Technical and Theoretical Publishing House, 1934 .-- 164 p.
• Privalov I.I. Subharmonic functions. - M .; L .: ONTI NKTP USSR, 1937. - 199 p. - (Mathematics in monographs).
  • Subharmonic functions. - 2nd ed. - M .: URSS, 2011 .-- 200 p. - ISBN 978-5-397-02124-1 .
• Privalov I.I. Integral equations. - 2nd, rev. ed. - M .; L .: ONTI NKTP USSR, 1937 .-- 248 p.
• Privalov I.I. Analytical geometry. - 11th ed. - M .; L .: GONTI, 1938 .-- 232 p.
• Privalov I.I. Boundary properties of unique analytic functions. - M .: Moscow State University, 1941 .-- 206 p.

Some Articles

• Privalov I.I. Properties of series in orthogonal functions // Mat. Sat - 1914. - T. 29 , No. 2 . - S. 182-185 .
• Privalov I. I. On the convergence of the series of Sturm - Liouville and Légendre // Communication. Kharkov. mate. Society The second ser. - 1917. - T. 15 , No. 3 . - S. 148-160 .
• Privalov I.I. Integral Cauchy // Proceedings of the Phys.-Math. Faculty of Saratov University. - 1918. - T. 11 , No. 1 .
• Luzin N. N. , Privalov I. I. Sur l'unicité et la multiplicité des fonctions analytiques // Compt. Rend. Acad. Sci . - 1924. - Vol. 178. - P. 456-449.
• Luzin N. N. , Privalov I. I. Sur l'unicité et multiplicité des fonctions analytiques // Ann. École Norm . - 1925. - Vol. 42. - P. 143-192.
• Privalov I. I. On the convergence of conjugate trigonometric series // Mat. Sat - 1925. - T. 32 , No. 2 . - S. 357-363 .
• Privalov I. I. On a boundary value problem of subharmonic functions // Matem. Sat - 1934. - T. 41 , No. 1 . - S. 3-10 .
• Privalov I. I. Applications of the concept of a harmonic measure of a set to some problems of function theory // Mat. Sat - 1938. - T. 45 , No. 3 . - S. 527-534 .

• Bermant A.F. , Markushevich A.I. Theory of functions of a complex variable // Mathematics in the USSR for thirty years. 1917-1947 / Ed. A. G. Kurosh , A. I. Markushevich , P. K. Rashevsky . - M.-L .: Gostekhizdat , 1948 .-- 1044 p. - S. 319-414.
• Kolyagin Yu.M., Savvina O.A. Dmitry Fedorovich Egorov: The path of a scientist and a Christian. - M .: PSTGU, 2010 .-- 302 p. - 1000 copies. - ISBN 978-5-7429-0611-7 .
• Stepanov V.V. Ivan Ivanovich Privalov (1891–1941) (obituary) // Proceedings of the USSR Academy of Sciences. The series is mathematical. - 1941. - T. 5 , No. 6 . - S. 389-394 .

• Profile of I. I. Privalov on the official website of the RAS
• Privalov Ivan Ivanovich - list and electronic versions of publications on the portal Math-Net.Ru
• Privalov Ivan Ivanovich (neopr.) . Chronicle of Moscow University . Date of treatment November 27, 2017.