Iossif Vladimirovich Ostrovskii

Born: 6 April 1934 in Dnepropetrovsk, Ukraine

Let us first note that Iossif Vladimirovich Ostrovskii's first name sometime appears as Iosif (as in [2] and [4]). He studied at a High School in Kramatorsk, Donetsk region [4]:-
His mathematical talent manifested itself in the seventh grade, when a long illness forced him to stay at home and he took a keen interest in reading mathematics textbooks by Andrei Petrovich Kiselev. In a month he had studied the whole program for the next two years. Great support in his desire to become a mathematician was given to him by his mathematics teacher in the 9th and 10th grades, Mariya Aronovna Fishkina, a former student of Mark Grigorievich Krein.
He graduated from the Kramatorsk High School in 1951 and entered the Faculty of Physics and Mathematics of Kharkov State University. This was an exceptionally strong Faculty with a host of leading mathematicians teaching there. For example, during Ostrovskii's student years the staff included: Naum Il'ich Akhiezer who held the Chair of the Theory of Functions, Anton Kazimirovich Suschkevich (1889-1961) who was Head of Algebra and Number theory, Yakov Pavlovich Blank (1903-1988), Gershon Ikhelevich Drinfeld (1908-2000) who was Head of the Mathematics Department and Deputy Director of the Kharkov Institute of Mathematics (his son Vladimir Gershonovich Drinfeld was awarded a Fields Medal in 1990), Boris Yakovlevich Levin, Vladimir Aleksandrovich Marchenko, Aleksandr Yakovlevich Povzner, and Aleksei Vasilevich Pogorelov. The teacher who influenced him most was Boris Yakovlevich Levin. It was in 1954 that Levin organised a research seminar on function theory, and Ostrovskii became one of its most active participants.

Ostrovskii graduated from Kharkov State University in 1956 and began undertaking research advised by Levin. He submitted his thesis The relation between the growth of a meromorphic function and the distribution of its values with respect to the arguments (Russian) in 1959 and was awarded his Master's degree (equivalent to a Ph.D.). He already had a number of published papers: A generalization of a theorem of M G Krein (Russian) (1957); and On meromorphic functions taking certain values at points lying near a finite system of rays (Russian) (1958). In these, and papers which he wrote in the following couple of years, he studied the connection between the growth of a meromorphic function and the distribution of its values by arguments. Some of his work was undertaken jointly with Levin and they wrote papers such as The dependence of the growth of an entire function on the distribution of zeros of its derivatives (Russian) (1960). In this paper they addressed the Polya-Wiman problem which relates to necessary and sufficient conditions that the zeros of all derivatives of a real entire function with real zeros lie on the real axis.

From 1958 Ostrovskii taught at Kharkov University, becoming the head of the Department of Function Theory in 1963. He was awarded a D.Sc. in 1965 for his thesis The asymptotic properties of entire and meromorphic functions and some of their applications (Russian). However, around this time some of his research began to take another direction, in particular he started looking at problems in analytic probability theory. He published papers such as Some theorems on decompositions of probability laws (Russian) (1965), On factoring the composition of a Gauss and a Poisson distribution (Russian) (1965), A multi-dimensional analogue of Ju V Linnik's theorem on decompositions of a composition of Gaussian and Poisson laws (Russian) (1965), and Decomposition of multi-dimensional probabilistic laws (Russian) (1966). To obtain these results, Ostrovskii had proved a stronger version of the Wiman-Valiron theorem on the behaviour of an entire function in a neighbourhood of points where its modulus attains the maximum value on the circle.

A collaboration between Ostrovskii and Anatolii Asirovich Goldberg led to important results. This came about since Levin examined Goldberg's Candidate's Thesis (equivalent to a Ph.D.) Some Problems of Distribution of Values of Meromorphic Functions in 1955 at Lvov University. This led to Goldberg collaborating with Levin's colleagues at Kharkov University, in particular with Ostrovskii. Their first joint papers were Some theorems on the growth of meromorphic functions (Russian) (1961) and New investigations on the growth and distribution of values of entire and meromorphic functions of genus zero (Russian) (1961). Another joint paper Application of a theorem of W Hayman to a question in the theory of expansions of probabilistic laws (Russian) (1967) was followed by the classic joint monograph The distribution of values of meromorphic functions (Russian) (1970). Here is a short extract of a review of this book by Walter Hayman:-

Nevanlinna theory has made considerable progress in the 50's and 60's, progress to which the authors of the present book have made distinguished contributions. Their book is detailed and authoritative, and there is little of importance in the subject of value distribution of functions meromorphic in the plane that is missing from this book and that cannot be found in the earlier books on the subject. The subject matter is illustrated at every stage by subtle and detailed examples -some of which are here published for the first time and some of which are not easily accessible elsewhere. ... All function theorists are indebted to the authors for this comprehensive and scholarly work.
Goldberg and Ostrovskii explain their aims in writing the monograph in a Preface:-
In this book ... the main attention is concentrated on the problems internal to the value distribution theory, which include the following problems: (i) To what extent the main inferences of Nevanlinna's theory have final character and cannot be improved further; (ii) What properties of Picard's exceptional values are preserved for a wider class of exceptional values considered in the value distribution theory; (iii) Which are the connections between Nevanlinna's characteristics and other quantities characterizing asymptotic properties of entire and meromorphic functions; (iv) Study of asymptotic properties and value distribution of meromorphic functions belonging to some special classes which are on one hand sufficiently narrow to give new information not implied by general theorems, and on the other hand sufficiently wide for being of interest for the general theory; (v) Study of the value distribution with respect to arguments (not only with respect to moduli as in classical Nevanlinna theory). We pay great attention to examples of functions with "exotic" properties. Without them the reader will get a restricted image of the theory under consideration. Examples of functions having unusual properties play in the theory a role as important as counterexamples do in real analysis.
In 1972 Ostrovskii published another important monograph, this time in collaboration with Yuri Vladimirovich Linnik. In a review of this book, with title Decompositions of random variables and random vectors (Russian), R Cuppens wrote:-
... this book is absolutely essential for any researcher interested in this field, or more generally by the elementary probability theory. It is to be hoped that a translation in a language more accessible appear quickly.
Indeed, the Russian text was translated into English and published by the American Mathematical Society in 1977 with the title Decomposition of random variables and vectors. Ostrovskii's 1970 book with Goldberg was also translated into English but this did not appear until 2008. Again the publication was by the American Mathematical Society and this impressive book had an appendix giving a survey of the results obtained after 1970, with extensive bibliography.

Ostrovskii was appointed to head the Department of Function Theory at the Low Temperature Physics and Technology Institute of the Ukrainian Academy of Sciences in 1986. He did not give up his chair at Kharkov University where he continued to work on a part-time basis. In 1995 he was appointed as a professor in the Department of Mathematics of Bilkent University in Ankara, Turkey. In 1996 he published the book Complex Analysis. Ostrovskii gives the following description of its contents:-

The first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications. It includes the fundamental notions, methods and results on the growth of entire functions and the distribution of their zeros, the Rolf Nevanlinna theory of distribution of values of meromorphic functions including the inverse problem, the theory of completely regular growth, the concept of limit sets for entire and subharmonic functions. The authors describe the applications to the interpolation by entire functions, to entire and meromorphic solutions of ordinary differential equations, to the Riemann boundary problem with an infinite index and to the arithmetic of the convolution semigroup of probability distributions. Polyanalytic functions form one of the most natural generalizations of analytic functions and are described in Part II. They emerged for the first time in plane elasticity theory where they found important applications (due to Kolossof, Mushelishvili etc.). This contribution contains a detailed review of recent investigations concerning the function-theoretical peculiarities of polyanalytic functions (boundary behaviour, value distributions, degeneration, uniqueness etc.). Polyanalytic functions have many points of contact with such fields of analysis as polyharmonic functions, Nevanlinna Theory, meromorphic curves, cluster set theory, functions of several complex variables etc.
There are many other areas to which Ostrovskii has made a major contribution. For example in the mid 1970s he collaborated with Vladimir Aleksandrovich Marchenko studying the spectrum of a Hill operator. In the late 1970s he studied complex-valued Borel measures on the real axis. He continued to work on this topic with his student Alexandr M Ulanovskii and they surveyed their results in this area in the joint paper Classes of complex-valued Borel measures than can be uniquely determined by restrictions (1989). In the 1980s Ostrovskii wrote a number of papers on the asymptotic behaviour of entire functions that are characteristic functions of probability measures. In the 1990s he published a number of papers on the Riemann boundary-value problem with an infinite index. In the 2000s he wrote On the zeros of tails of power series (2000) and On the zero distribution of remainders of entire power series (2001).

The article [2] is written by a number of mathematicians who have been taught by Ostrovskii so are in the best possible position to explain his merits as a teacher and advisor:-

Iosif Vladimirovich combines the gifts of a researcher with the talents of a teacher. He has lectured for over thirty years at Kharkov University. His lectures, distinguished by a careful depth of thought and a thoroughness of material, bear the stamp of the lecturer's character. In them we can easily sense the deep-rooted enthusiasm and keenness of the man. Iosif Vladimirovich has taught many pupils, and three of them have become doctors of science. Under his supervision twenty Ph.D. dissertations have been defended. Iosif Vladimirovich gives a great deal of attention to his students. He generously shares his scientific ideas, and knows how to get on with both the beginner in research and the more advanced researcher. All those who have had dealings with him know well his readiness and ability to help with both advice and action, his attentiveness, sense of duty, and his adherence to principles.
Outside mathematics, one of Ostrovskii's hobbies involves sailing [4]:-
Many people know Ostrovskii as an irreplaceable captain of numerous trips lasting several days on the rivers Volga, Desna, Sura, Vorona, Yuruzan, and others, and remember how his calm confidence and experience were a great support to wet beginners who had their spirits dampened after a first leak in a boat. However, accidents were seldom.

Article by: J J O'Connor and E F Robertson

January 2014
MacTutor History of Mathematics