Mark Grigorievich KREIN
Born: 3 April 1907 in Kiev, Ukraine
Died: 17 Oct 1989 in Odessa,
Mark G Krein's father was involved in the wood trade
which meant that the family had little money. The fact that the family were
Jewish meant that Krein grew up in an atmosphere of persecution. This was also
highly significant for Krein's subsequent career, for discrimination against
Jews in the Ukraine was bad and, by misfortune for Krein, was particularly bad
in Odessa where he lived from the age of 17.
Krein showed a remarkable talent for mathematics at a young
age. By the time he reached 14 years of age he was already attending research
seminars in mathematics in Kiev. However, Krein never completed his
undergraduate degree for he left his home in Kiev when he was 17 years old and
ran away to Odessa. Despite the lack of an undergraduate degree, his talents
were clearly visible to the mathematicians at Odessa University and, in 1926,
Krein was accepted for doctoral studies under Chebotaryov.
Chebotaryov himself was not in the happiest of positions for,
after working at Odessa University, he had accepted a permanent post in Moscow
in 1924. The political situation surrounding this appointment induced him to
leave Moscow and return to Odessa after only a few months. Krein therefore began
his doctoral studies well aware of the difficulties of the time.
In 1928 Chebotaryov left Odessa and became professor at Kazan
University. Krein completed his doctorate at Odessa in the following year and
remained on the staff at the university building up one of the most important
centres for functional analysis research in the world. During this time he
worked on topics such as Banach spaces, the moment problem, integral equations
and matrices, and on spectral theory for linear operators. As Osilenker writes
in  and :-
In the creative legacy of M G Krein a large place is
occupied by the moment problem and the study of associated Jacobian
Krein's work on the moment problem, which played such an
important part in his mathematical development, is discussed in detail in 
Kolmogorov had laid the foundations for the study of extremal
problems in 1935 and Krein began to work on extremal problems for the class of
differentiable periodic functions. Together with N I Akhiezer, Krein made a
major contribution to this field in 1937.
In 1941 Krein had to leave Odessa when the university was
evacuated as the German armies advanced. He was appointed as professor of
theoretical mechanics at Kuibyshev Industrial Institute but he returned to
Odessa in 1944. However, soon after taking up his post again he was dismissed.
Gohberg writes in :-
[Krein] was accused of Jewish nationalism,
presumably for having had too many Jewish students before the War. This
accusation was certainly included in his classified file and was presumably
held against him all his life. ... He was not allowed to have Jewish students
and was deprived of a university base.
Not only was Krein dismissed but the whole of the functional
analysis school at Odessa was closed down. Potapov, who had been one of Krein's
non-Jewish students, tried hard to influence the university authorities to
reverse their decisions. He wrote:-
The leaders of the university have to correct their
mistakes and to revive immediately the famous traditions of the Odessa School
of Mathematics. The Faculty of Physics and Mathematics has to become active
again, as a really creative centre of scientific and mathematical thought in
our city ....
Krein was not reinstated, however, but held the chair of
theoretical mechanics at Odessa Marine Engineering Institute from 1944. Also
from 1944, he held a part-time post as head of the functional analysis and
algebra department at the Mathematical Institute of the Ukranian Academy of
Science in Kiev. This latter position came to a sudden end in 1952 when he was
dismissed for a second time. Officially the reason given was that he did not
live in Kiev, but in reality it seems more likely that the accusation of Jewish
nationalism in his classified file was again the reason.
Although the 1940s must have been difficult times for Krein,
his mathematical research did not suffer. Among other important work, Krein
wrote eight papers on harmonic analysis and representation theory in the 1940s.
In these papers he studied the use of algebras of operators applied to obtain
results on positive definite kernels and functions. He also studied analysis on
homogeneous spaces and duality theorems.
From 1954 until his retirement Krein occupied the chair of
theoretical mechanics at the Odessa Civil Engineering Institute. During the
1940s and 1950s there were many unsuccessful attempts to have Krein and his
students reinstated at Odessa University but all attempts failed.
During the many years of very active research Krein had around
him a group of very active mathematicians although this group was based more on
an informal arrangement than that of a proper research group. This group
provided him with strong support, frequently meeting in Krein's own house. For
example one of the Jewish student he ahd supervised before World War II was
Livsic and he, like Krein, was not welcome back at Odessa University after the
War. Livsic, again like Krein, did return to Odessa, teaching at the
Hydrometerological Institute until 1957 and forming part of Krein's unofficial
research group in Odessa. As well as Krein's house, the group often met at the
Scientists' Club in Odessa and, in , Thomas Kailath describes a visit he
made to Odessa where he talked at the Scientists' Club at the end of 1984. Despite the support of those around him, Krein did have to work
at a mathematical disadvantage in one sense, however, for he was not allowed to
travel abroad and so was unable to attend international conferences that many
mathematicians feel to be almost essential for someone so preeminent at an
International recognition came to Krein despite his inability
to visit centres of mathematical research around the world. In 1968 the American
Academy of Arts and Sciences elected him an honorary member, and he was elected
a Foreign Member of the National Academy of Sciences in 1979. Krein received
many other honours, but perhaps the most prestigious award made to him was the
Wolf Prize in Mathematics in 1982. After the years of discrimination on account
of being Jewish it must have been particularly pleasing to receive this Prize
from Israel. The citation for the prize summarises well the contribution that
Krein made to mathematics:-
His work is the culmination of the noble line of research
begun by Chebyshev, Stieltjes, Sergei Bernstein and Markov and continued by F
Riesz, Banach and Szego. Krein brought the full force of mathematical analysis
to bear on problems of function theory, operator theory, probability and
mathematical physics. His contributions led to important developments in the
applications of mathematics to different fields ranging from theoretical
mechanics to electrical engineering. His style in mathematics and his personal
leadership and integrity have set standards of excellence.
Gohberg writes of the quality and style of Krein's work in
He is the author of more than 270 papers and
monographs of unsurpassed breadth and quality. ... A profound intrinsic unity
and close interlacing of general abstract and geometrical ideas with concrete
and analytical results and applications and characteristic of Krein's
Despite a life of persecution, in which he often feared arrest,
Krein remained enthusiastic, friendly and kind, showing great mathematical
generosity towards his students and colleagues. Towards the end of his life,
however, the struggle which he continually had to make took its toll and he
suffered from depression which became worse after the death of his wife.
J. J. O'Connor, E. F. Robertson
References for Mark Krein:
- V M Adamjan, Ju M Berezans`kii, N N Bogoljubov, I S Iohvidov, A N Kolmogorov, M A Lavrentiev and Ju A Mitropol`skii, Mark Grigorievich Krein (on the occasion of his seventieth birthday) (Russian), Uspekhi Mat. Nauk 33 3(201) (1978), 197-203.
- N I Ahiezer, Ju M Berezans`kii, I S Iohvidov, Ju A Mitropol`skii and V P Potapov, Mark Grigorievich Krein (Russian), Ukrain. Mat. Z. 19 (5) (1967), 114-118.
- D Z Arov, The influence of V P Potapov and M G Krein on my scientific work, in Matrix and operator valued functions, Oper. Theory Adv. Appl. 72 ( Basel , 1994), 1-16.
- D Z Arov, Yu M Berezanskii, N N Bogolyubov, V I Gorbachuk, M L Gorbachuk, Yu A Mitropol`skii and L D Faddeev, Mark Grigorievich Krein (on the occasion of his eightieth birthday) (Russian), Uspekhi Mat. Nauk 42 4(256) (1987), 201-206.
- T Ya Azizov, Yu P Ginzburg and G Langer, On the work of M G Krein in the theory of spaces with an indefinite metric, Ukrainian Math. J. 46 (1-2) (1994), 3-14.
- T Ya Azizov, Yu P Ginzburg and G Langer, On the work of M G Krein in the theory of spaces with an indefinite metric (Russian), Ukrain. Mat. Zh. 46 (1-2) (1994), 5-17.
- Yu M Berezans`kii, Marko Grigorovich Krein, Ukrainian Math. J. 46 (3) (1994), 149-150.
- Yu M Berezans`kii, Marko Grigorovich Krein (Ukrainian), Ukrain. Mat. Zh. 46 (3) (1994), 146.
- Yu M Berezanskii, B Ya Levin, V A Marchenko, Yu A Mitropol`skii, I V Ostrovskii, Mark Grigorievich Krein, Ukrainian Math. J. 42 (4) (1990), 511.
- Yu M Berezanskii, B Ya Levin, V A Marchenko, Yu A Mitropol`skii, I V Ostrovskii, Mark Grigorievich Krein (Russian), Ukrain. Mat. Zh. 42 (4) (1990), 576.
- Bibliography of Mark Grigorievich Krein, in Orthogonal matrix-valued polynomials and applications, Tel Aviv, 1987-88, Oper. Theory Adv. Appl. 34 ( Basel , 1988), 1-24.
- N N Bogoljubov, I C Gohberg, G E Silov, Mark Grigorievich Krein : On his sixtieth birthday (Russian), Uspekhi Mat. Nauk 23 3 (141) (1968), 197-214.
- I Gohberg, Mark Grigorievich Krein, 1907-1989, Notices Amer. Math. Soc. 37 (3) (1990), 284-285.
- I Gohberg, Mark Grigorievich Krein : recollections, in Dedicated to the memory of Mark Grigorievich Krein (1907-1989), Integral Equations Operator Theory 30 (2) (1998), 123-134.
- T Kailath, A visit to M G Krein, in Dedicated to the memory of Mark Grigorievich Krein (1907-1989), Integral Equations Operator Theory 30 (2) (1998), 135-139.
- T Kailath, To the friends and admirers of Professor M G Krein, Gaz. Math. No. 32 (1987), 62-67.
- A N Kolmogorov , M A Krasnosel`skii, Mark Grigorievich Krein (on his fiftieth birthday) (Russian), Uspekhi Mat. Nauk (N.S.) 13 (1958), 213-224.
- B Ya Levin, Reminiscences of Mark Grigorievich Krein, Ukrainian Math. J. 46 (3) (1994), 318-323.
- B Ya Levin, Reminiscences of Mark Grigorievich Krein (Russian), Ukrain. Mat. Zh. 46 (3) (1994), 305-309.
- Mark Grigorievich Krein, Functional Anal. Appl. 24 (2) (1990), 85.
- Mark Grigorievich Krein (Russian), Funktsional. Anal. i Prilozhen. 24 (2) (1990), 1-2.
- Yu A Mitropol`skii, Mark Grigorievich Krein, Ukrainian Math. J. 46 (1-2) (1994), 1-2.
- Yu A Mitropol`skii, Mark Grigorievich Krein (Russian), Ukrain. Mat. Zh. 46 (1-2) (1994), 3-4.
- Yu A Mitropol`skii, Yu M Berezanskii, M L Gorbachuk and V I Gorbachuk, Mark Grigorievich Krein (on the occasion of his eightieth birthday) (Russian), Ukrain. Mat. Zh. 39 (2) (1987), 244.
- A A Nudel`man, The work of M G Krein on the moment problem, Ukrainian Math. J. 46 (1-2) (1994), 62-74.
- A A Nudel`man, The work of M G Krein on the moment problem (Russian), Ukrain. Mat. Zh. 46 (1-2) (1994), 63-75.
- B P Osilenker, M G Krein`s range of ideas in the theory of orthogonal polynomials, Ukrainian Math. J. 46 (1-2) (1994), 75-86.
- B P Osilenker, M G Krein`s range of ideas in the theory of orthogonal polynomials (Russian), Ukrain. Mat. Zh. 46 (1-2) (1994), 76-86.
- I V Ostrovskii, The investigations of M G Krein in the theory of entire and meromorphic functions and their further development, Ukrainian Math. J. 46 (1-2) (1994), 87-100.
- I V Ostrovskii, The investigations of M G Krein in the theory of entire and meromorphic functions and their further development (Russian), Ukrain. Mat. Zh. 46 (1-2) (1994), 87-99.
- L I Vainerman, The papers of M G Krein in representation theory and harmonic analysis on topological groups (Russian), Ukrain. Mat. Zh. 46 (3) (1994), 198-211.