Aleksei Alekseevich Dezin

Born: 23 April 1923 in Moscow, Russia
Died: 4 March 2008 in Moscow, Russia

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Aleksei Alekseevich Dezin's father, also named Aleksei Alekseevich Dezin, was an economist who had graduated from St Petersburg, and his mother was Alisa Eduardovna; both parents were of German descent. Aleksei Alekseevich senior was an important figure in the currency reforms of the 1920s when the chervonet, based on the gold standard, was introduced to replace the rouble which had become worthless. These currency reforms were a vital step in the New Economic Policy. The authors of [12] write about Aleksei Alekseevich junior's extremely difficult upbringing:-
Throughout his whole life, Aleksei Alekseevich Dezin kept sincere love and gratitude to his parents, whom he lost in early childhood. His father was arrested in 1936 and killed in 1937, and his mother was arrested in 1937 as a family member and condemned to eight years of labour camps. The 14-year old boy was sent to children's home and then arrested and condemned to five years in a labour colony. He served his sentence at a lumber site in the Kolyma region, was released in December 1942, and was drafted in early 1943. Until the end of the war, Dezin served in the army in the Far East region. During the war against Japan, he participated in the forced crossing of the Amur river near Blagoveshchensk and was awarded the medal "For Victory over Japan."
For those unaware of Russian history, it may seem strange that someone obviously intimately connected with the Communist Party should be treated in this way. However, from 1936 to 1938, Joseph Stalin purged many members of the leadership of the Party (in addition to hundreds of thousands of others accused of political crimes) who were executed by shooting or sent to Gulag labour camps. The majority of Gulag camps were positioned in extremely remote areas of north-eastern Siberia along the Kolyma river. In these camps, which involved gold mining, road building, and lumbering, conditions were extremely harsh. Dezin had only completed his ninth grade as school in 1937 when his mother was arrested and his education came to an end. After the war ended and he was released from the army, Dezin returned to Moscow where he completed his secondary education, graduating with the silver medal, after the ten year interruption.

In 1948 he entered the Faculty of Mechanics and Mathematics of Moscow State University, graduating in 1953. He continued to undertake research at Moscow State University advised by Sergei Lvovich Sobolev and was awarded his candidate's degree (equivalent to a Ph.D.) in 1956 for his thesis Boundary Value Problems for Symmetric Systems of Partial Differential Equations. He had begun writing research papers while still an undergraduate [12]:-

The hardship in youth did not break Dezin's character. Even during his student years, he actively participated in research.
Before the award of his doctorate he had published several papers in Russian: On imbedding theorems and the problem of continuation of functions (1953); The second boundary problem for the polyharmonic equation in the space W2m (1954); Mixed problems for certain symmetric hyperbolic systems (1956); Concerning solvable extensions of the first order partial linear differential operators (1956); and Mixed problems for certain parabolic systems (1956). These [14]:-
... papers concerned extension of functions, embedding theorems, and also an analysis of conditions for solubility of the second boundary-value problem for polyharmonic equations. Already in his diploma work he developed a technique involving operators of averaging with variable radius, which even at present remains an effective tool in the theory of extension of functions and in the theory of boundary-value problems, in investigations of the problem of when weak and strong solutions coincide.
Of course the Russian doctorate (similar to the German habilitation) is a higher degree and Dezin continued to undertake research with this as his goal. While doing so, from 1956, he taught in the Department of Mathematics at the Moscow Institute of Physics and Technology and, from the following year, undertook research at the Steklov Mathematical Institute of the USSR Academy of Sciences. In 1961 he defended his thesis Invariant Differential Operators and Boundary Value Problems and, following the award of a D.Sc., he was promoted in 1962 to Professor in the Department of Computational Mathematics in the Faculty of Aerodynamics of the Moscow Institute of Physics and Technology. He continued to hold his position in the Steklov Mathematical Institute for the rest of his life but he retired from his position at the Moscow Institute of Physics and Technology in 1991. However in 1994, when over seventy years of age, Dezin was appointed as a professor in the Department of General Mathematics in the Faculty of Numerical Mathematics and Cybernetics at Moscow State University.

We have already noted Dezin's 1961 thesis Invariant Differential Operators and Boundary Value Problems. This was written in a period when he was publishing a particularly outstanding series of papers on invariant systems of first-order partial differential equations on smooth Riemannian manifolds. These had the ultimate aim of trying to understand the structure of the Cauchy-Riemann equations in the plane. These papers include Existence and uniqueness theorems for solutions of boundary problems for partial differential equations in function spaces (1959), Boundary value problems for invariant elliptic systems (1960), and Invariant elliptic systems of equations (1960).

Most of the research that Dezin undertook during the rest of his career was presented first in papers and then in a number of monographs, so let us now look at these books. In 1980 he published the Russian book General questions of the theory of boundary value problems. An English translation with title Partial differential equations. An introduction to a general theory of linear boundary value problems was published in 1987. Howard Levine writes [5]:-

The author has intended this book to be an introduction to a general theory of boundary value problems for linear partial differential equations accessible to graduate students as well as researchers. ... In simplest terms, this is a book about separation of variables in partial differential equations. More accurately, the book may be considered an introduction to the use of spectral theory in solving initial- and two- point boundary value problems for ordinary differential equations with unbounded operator coefficients. .... Although the author comments in the Preface that boundary value problems of the form he considers are of interest in mathematical physics, in the body of the text he gives scanty reference to real physical examples of such problems. ... I found that in many places the author has taken the trouble to explain things very well. The examples he discusses are interesting and instructive. ... he has made an important contribution to the literature on this subject.
Dezin's next little book of 63 pages Equations, operators, spectra (1984) shows him to be a skilful and an innovative expositor. F-H Vasilescu explains in a review from which we present some extracts:-
Assume that you meet someone who knows only the elements of mathematics, for instance how to solve a system of two linear equations with two unknowns, but is eager to learn more, and you want to inform this person about the meaning of spectral theory of linear operators. Of course, your task will not be too easy. The present booklet is an attempt along this line, addressed to a large and heterogeneous public. The author imagines an ideal reader who asks questions, which are answered promptly, with supplementary explanations (such an interlocutor occurs in the first and the second chapter of the work, but only for a short time in the third). The author's comments lead to new questions and so on. The potential reader is transported from very simple systems of linear equations to concepts as complex as that of linear space, invertible operator, eigenvalue and eigenvector, norm, adjoint, unitary and selfadjoint operator. In connection with the commutativity, even Lie algebras are mentioned. ... The author has done a careful job and, at the same time, conducted an interesting experiment. He shows a special gift for making complicated facts look simple.
In 1990 Dezin published Multidimensional analysis and discrete models in Russian, an English translation being published five years later. Dezin gives his own summary of the book:-
This book is devoted to the description of basic structures of multidimensional analysis and the consideration of internally determined discrete models of problems in analysis and mathematical physics. This has to do not simply with the approximation of a given continuous object, but with the construction of its analogue, starting from concepts admitting a discrete treatment. We describe special difference models of equations of mathematical physics, models of boundary value problems and objects of quantum mechanics. We focus on differential operators on Riemannian manifolds, the interpretation from this point of view of classical vector analysis, and also its generalizations.
Jules Beckers, reviewing the English translation, is critical, however, writing:-
Addressed essentially to mathematical physicists, such a book asks for too many complementary readings in order to become interesting.
Dezin had many other talents and interests outside mathematics. He spoke English fluently and read easily in several languages which included German, French, Italian and Greek. His literary talents were particularly seen in his poetic talents which he used both in translating poetry and writing his own. He was married to Nataliya Borisovna and their home [12]:-
... was a gathering place for a wide circle of their friends, including many distinguished mathematicians and humanitarians and Dezin's students, who were attracted by the intellectual atmosphere.
The authors of [10] note that he:-
... was remarkable for his invariable kindness, sympathy, modesty, broad knowledge, and the diversity of his interests.

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

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JOC/EFR November 2010
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