In memory of Vitalii Yakovich Skorobogat'ko (18 July 1927–7 April 1996)

Abstract

Be ready to die, but plow your field," was Vitali Yakovich's favorite saying, one he frequently repeated in difficult situations and to which he held fast to the final days of his life. When he learned that the end was near, he courageously and firmly brought his research into a form suitable for publication, conducted his seminars, gave new problems to his students and suggested means of solving them. More concerned for his students than for himself, he gave a great deal of attention to preparing for publication the articles that appear in the present number. Although the end was not completely unexpected, it nevertheless came far too soon...Vitalii Yakovich was born on 18 July 1927 in Kiev. He began his mathematical education at Moscow University in the important war year of 1945, continuing it at the University of L'viv, where he received his diploma in 1951 with a recommendation for graduate study. His early years in L'viv coincided with the growth of the L'viv school of partial differential equations led by Prof. Ya. B. Lopatins'kii, under whose influence Skorobogat'ko's research interests were already beginning to form in his undergraduate years. A strong influence on his formation as a scholar and leader were Profs. M. Zarits'kii and V. Levits'kii, of whom Vitalii Yakovich always spoke with deep gratitude. After finishing his kandidat dissertation, "Uniqueness and existence of solutions of certain boundary-value problems for a second-order differential equation of elliptic type" (1954) and his doctoral dissertation "Studies in the qualitative theory of partial differential equations" (1963), Vitalii Yakovich greatly enlarged the scope of his research. While continuing his research in the area of the qualitative theory of differential equations, he began to work in new areas connected with multidimensional generalization of continued fractions (branched continued fractions), and constructed a geometry in which a "line" is determined by n (n >_ 2) points ("multipoint" geometry). The results of his research found application in neighboring areas of science, especially in computational mathematics and theoretical physics.Skorobogat'ko always combined intensive research with the active preparation of teachers, devoting a great deal of attention to work with young mathematicians and his students. For nearly 30 years, 4 weekly research seminars were regularly conducted under his direction, uniting the participants into a creative mathematical group-the Skorobogat'ko research school. Among his students 7 have received the doctorate and 25 the kandidat degree, and they work in many areas of mathematics and theoretical and mathematical physics.He was always an active scholar, selflessly devoted to mathematics and to his native country and its people, not only a person of democratic, humanistic views, irreconcilable with authoritarianism, deference to rank, intimidation, or injustice, but also a person who systematically and firmly stood up for his principles, regardless of the consequences for himself.He taught us t...