Isaak Moiseevich Milin

Isaak Moiseevich Milin , Russian Исаак Моисеевич Милин , English transcription Isaak Moiseevich Milin, (born February 16, 1919 in Oster, Ukrainian SSR ; † November 17, 1992 in Saint Petersburg , Russian Federation ) was a well-known Soviet mathematician who was a specialist in the Areas of the geometric theory of the functions of complex variables (geometric function theory ) and applied mathematics. He was also a lieutenant colonel in the Soviet Union Air Force .

Milin Isaak Moiseevich

Biographical information

After graduating from school in 1937, IM Milin began studying mathematics at the Leningrad State University (Faculty of Mathematics and Mechanics). In connection with the outbreak of World War II , he continued his studies at the Leningrad Air Force Academy of the Red Army, which he graduated with honors in 1944. Here he has the qualification of both a mathematician and a Dipl.-Ing. (Mechanics) acquired. In addition, he received the rank of officer in the Air Force of the USSR. Since then, IM Milin has worked successfully in various teaching and scientific research institutes throughout his life. IM Milin defended his dissertation in 1950 under the academic supervision of Gennady Michailowitsch Golusin (1906–1952). He completed his habilitation in 1964 (Russian doctorate). In both his dissertation and his habilitation thesis he dealt with the development and application of methods of the geometric theory of the functions of complex variables. After demobilization from the armed forces of the USSR in 1976, IM Milin headed the research department (laboratory) for algorithmization and automation of technological processes in the Leningrad Research Institute MECHANOBR.

Scientific activity

A significant part of IM Milin's scientific activity is devoted to the important branch of complex analysis - the theory of regular , meromorphic and univalent (simple) functions and their connection with the problems of Taylor and Laurent coefficients. He is known for his area theorem, the estimates of coefficients and integral means, the Milin functionals, Milin's Tauber theorem, Milin's constant, and the Lebedev-Milin exponential inequalities. In 1949 IM Milin and Nikolai Andrejewitsch Lebedew (1919–1982) proved the hypothesis of Rogosinski (1939) about the coefficients of the Bieberbach-Eilenberg functions. In 1964, IM Milin received, in connection with his investigations into the famous Bieberbach conjecture from 1916, the best estimates for the coefficients of univalent functions for the previous 15 years. His results are contained in his monograph “Univalent functions and orthonormal systems” (1971) and, from a uniform point of view, all the mathematical results that were known at that time for systems of regular surface orthonormal functions are presented. IM Milin also put forward the conjecture that the sequence of logarithmic functionals (Milin functionals) constructed by him is not positive for any function from class S and emphasizes that this property leads to a proof of the Bieberbach conjecture . In 1984 the French-American mathematician Louis de Branges de Bourcia proved the Milin Hypothesis and thus also the Bieberbach Hypothesis. A second Milin's conjecture about the logarithmic coefficients of univalent functions, published in 1983, remains an unsolved problem. For many years, IM Milin has been actively involved in the development and application of methods of analysis and optimization for the solution of engineering problems. Among other things, he made a significant contribution to the practical application of mathematical methods for solving problems of the automatic control of technological processes in ore enrichment. IM Milin is the author of several textbooks and manuals for engineers.

Government awards

IM Milin was honored with fourteen awards from the Soviet government, including the medals for combat merit and for victory over Germany in the Great Patriotic War of 1941–1945 .

bibliography

• IMMilin, NALebedew. About coefficients of some classes of analytic functions. Docl. Akad. Nauk USSR (1949), Volume 67, pp. 221-223 (Russian).
• NALebedew, IMMilin. About coefficients of some classes of analytic functions. Mat. Sb., (1951), Vol. 28 (70), № 2, pp. 359-400 (Russian).
• IMMilin. The area method in the theory of univalent functions. Docl. Akad. Nauk USSR, 154 № 2 (1964), pp. 264-267 (Russian); English transl .: Soviet Math. Dokl. 5: 78-81 (1964).
• NALebedew, IMMilin. About an inequality, Vestnik Leningrad. Univer., 20 (19), (1965), pp. 157-158 (Russian).
• IMMilin. An estimate of the coefficients of univalent functions. Docl. Akad. Nauk USSR, 160, № 4 (1965), pp. 769-771 (Russian); English transl .: Soviet Math. Dokl. 6: 196-198 (1965).
• IMMilin. About the coefficients of the univalent functions. Docl. Akad. Nauk USSR, 176 (1967), pp. 1015-1018 (Russian); English transl .: Soviet Math. Dokl. 1967, 8: 1255-1258.
• IMMilin. The method of surfaces for univalent functions in finitely connected areas. Trudy Mat. Inst. WASteklow Akad. Nauk USSR, 94, (1968), pp. 90-122 (Russian); English transl .: Proc. Steklov Inst. Math. 94: 105-142 (1968).
• IMMilin. About the neighboring coefficients of the univalent functions. Docl. Akad. Nauk USSR 180, № 6 (1968), pp. 1294-1297 (Russian); English transl .: Soviet Math. Dokl. 1968, 9: 726-765.
• IMMilin. Hayman's regularity theorems for the coefficients of univalent functions. Docl. Akad. Nauk USSR, 192, № 4 (1970), (Russian); English transl .: Soviet Math. Dokl. 1970, 11: 724-728.
• IMMilin. Methods of searching for extremum values ​​of functions of several variables, Moscow, Wojenizdat, (1971), (Russian).
• IMMilin, Ju.A.Litwinchuk. The estimation of the outer arcs in the case of univalent images. Matem. Zametki, 18: 3 (1975), pp. 367-378 (Russian).
• IMMilin. Univalent functions and orthonormal systems. Moscow, Nauka, 1971, (Russian); English transl .: Amer. Math. Soc. Providence, RI (1977).
• IMMilin. A property of the logarithmic coefficients of univalent functions. Metric questions of function theory. Naukova Dumka, Kiev (1980), pp. 86-90 (Russian).
• IMMilin. The hypothesis about the logarithmic coefficients of the univalent functions. Analytical number theory and function theory. Vol. 5, Zap. Nautschn. Sem. Leningrad Department d. Math. Inst. WASteklow, 125 (1983), pp. 135-143 (Russian); English transl .: J. Soviet Math. 26 (6) (1984), 2391-2397.
• IM Milin: Comments on the proof of the conjecture on logarithmic coefficients, in Albert Baernstein, David Drasin, Peter Duren, Albert Marden: The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof, American Mathematical Society (1986), p 109-112 (English).
• VIBraun, VGDjumin, IMMilin, VSProzuto. Balance of metals. Computer: Information grant, Moscow: Nedra, (1991), (Russian).
• Ju.E. Alenitsyn, AZ Grinshpan, EG Emelyanov, IMMilin. Goluzin's school of geometric theory of functions of complex variables. Preprint (1990). Functional analysis (Uljanowsk), 37 (1999), pp. 3-14 (part 1), pp. 15-28 (part 2) (Russian).

literature

• AAAlexandrov, Ju.E.Alenizin, VIBeliy, VVGorjaynow, AZGrinschpan, V.Ja.Gutljansky, SLKruschkal, NMMatweew, VIMilins, IPMitjuk, SVNikitin, VPOdinez, Ju.G. Reshetnyak, PM Tamrasov., NASchirokow., NASchirokow. ISAAK MOISEEWITSCH MILIN (Nekrolog), usp. Math. Nauk (1993), Vol. 48, No. 4 (292), pp. 167-168 (Russian).
• AZGrinshpan. The Bieberbach Conjecture and Milin's Functionals. American Mathematical Monthly, Vol. 106 (1999), No. 3, 203-214 (English).
• Handbook of Complex Analysis: Geometric Function Theory (Edited by R. Kühnau), V.1 (2002), V.2 (2005), North-Holland, Amsterdam, (English).

Web links

• mathnet.ru