Petunin, Yuri Ivanovich

Born September 30, 1937 in the city of Michurinsk . In 1954 he entered the Faculty of Physics and Mathematics of the Tambov State Pedagogical Institute, where the supervisor of studies was the talented teacher and mathematician D. L. Pikus. According to his recommendation, in 1960 he entered the graduate school of Voronezh State University with Professor S.G. Crane, brother of the largest mathematician M.G. Crane. During the years of postgraduate studies, he is engaged in functional analysis, the study of which he began at scientific seminars led by D.L. By the picus. After graduating from the Tambov State Pedagogical Institute, he began to engage in scientific work in the field of functional analysis at Voronezh State University under the leadership of S. G. Krein . ^[1] In 1962 he defended his thesis, and in 1968 he became a doctor of physical and mathematical sciences. Since 1970, he worked as a professor at the Department of Computational Mathematics at Kiev State University .

Yu. I. Petunin made a significant contribution to the field of functional analysis, creating the theory of scales of Banach spaces ^[2] , the theory of characteristics of linear manifolds in conjugate Banach spaces ^[3] , and developed the interpolation theory with S. G. Krein and E. M. Semenov linear operators ^{[4] [5]} . He gave a solution to the Banach problem of normalized subspaces in conjugate Banach spaces ^[3] , solved the problem posed by well-known mathematicians Calderon and Lyons about interpolation in quotient spaces ^[4] .

Professor Petunin Yu. I. also worked hard and fruitfully in the field of pattern recognition , mathematical statistics and its applications to solving medical and biological problems, in particular to the problem of differential diagnosis of oncological diseases ^[6] . Among his most important results in mathematical statistics, one should mention a rigorous mathematical justification of the rule of thumb 3σ for single-mode distributions known since Gauss ^[7] . Vysochansky-Petunin’s Inequality , which has already become classic, has solved the problem that mathematicians have faced for more than 150 years. In the theory of pattern recognition, he constructed the theory of linear decision rules in which the questions of linear separability of any number of sets in n-dimensional spaces were studied in detail ^[8] .

In the last years of his life, Yuri Ivanovich returned to the field of functional analysis, with which he began his research. Together with his students, he successfully worked on the solution ^{[9] of the} twentieth Hilbert problem .

• Member of the American Mathematical Society
• It is listed in the book “Who Is Who In the World?” (“Who is Who in the World?”, USA).

Author of more than 400 scientific papers, including monographs

• Application of the theory of random processes in biology and medicine, Kiev: Naukova Dumka, 1981., 320 pp.
• Interpolation of linear operators, Providence, RI: American Mathematical Society, 1982. vii, 375 p., ISBN 0-8218-4504-7 (co-authored)
• Evidence Based Medicine. Application of statistical methods, 320 pp., ISBN 978-5-8459-1321-0 , DIALECTICS, 2008 (co-authored)
• Hilbert's Twentieth Problem. Generalized solutions of operator equations, 192 pp., ISBN 978-5-8459-1524-5 , DIALECTICS, 2009 (co-authored)

• Krein S. G. , Petunin Yu. I., Semenov E. M. Interpolation of linear operators. - M .: Nauka, 1978.- 400 p.