Mark Grigorievich Krein ( uk, Марко́ Григо́рович Крейн, russian: Марк Григо́рьевич Крейн; 3 April 1907 – 17 October 1989) was a Soviet mathematician, one of the major figures of the
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...
school of
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...
. He is known for works in
operator theory
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators ...
(in close connection with concrete problems coming from
mathematical physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
),
the problem of moments,
classical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
These theories are usually studied in ...
and
representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
.
He was born in
Kyiv
Kyiv, also spelled Kiev, is the capital and most populous city of Ukraine. It is in north-central Ukraine along the Dnieper, Dnieper River. As of 1 January 2021, its population was 2,962,180, making Kyiv the List of European cities by populat ...
, leaving home at age 17 to go to
Odessa
Odesa (also spelled Odessa) is the third most populous city and municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern shore of the Black Sea. The city is also the administrativ ...
. He had a difficult academic career, not completing his first degree and constantly being troubled by
anti-Semitic
Antisemitism (also spelled anti-semitism or anti-Semitism) is hostility to, prejudice towards, or discrimination against Jews. A person who holds such positions is called an antisemite. Antisemitism is considered to be a form of racism.
Antis ...
discrimination. His supervisor was
Nikolai Chebotaryov
Nikolai Grigorievich Chebotaryov (often spelled Chebotarov or Chebotarev, uk, Мико́ла Григо́рович Чеботарьо́в, russian: Никола́й Григо́рьевич Чеботарёв) ( – 2 July 1947) was a Ukrainia ...
.
He was awarded the
Wolf Prize in Mathematics in 1982 (jointly with
Hassler Whitney
Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes, and geometric integration t ...
),
but was not allowed to attend the ceremony.
David Milman
David Pinhusovich Milman (russian: Дави́д Пи́нхусович Ми́льман; 15 January 1912, Chechelnyk near Vinnytsia – 12 July 1982, Tel Aviv) was a Soviet and later Israeli mathematician specializing in functional analysis. He wa ...
,
Mark Naimark
Mark Aronovich Naimark (russian: Марк Ароно́вич Наймарк) (5 December 1909 – 30 December 1978) was a Soviet mathematician who made important contributions to functional analysis and mathematical physics.
Life
Naimark was b ...
,
Israel Gohberg
Israel Gohberg ( he, ישראל גוכברג; russian: Изра́иль Цу́дикович Го́хберг; 23 August 1928 – 12 October 2009) was a Bessarabian-born Soviet and Israeli mathematician, most known for his work in operator theory ...
,
Vadym Adamyan,
Mikhail Livsic and other known mathematicians were his students.
He died in Odessa.
On 14 January 2008, the memorial plaque of Mark Krein was unveiled on the main administration building of
I.I. Mechnikov Odessa National University.
See also
*
Tannaka–Krein duality
In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is a natural extension of Pontryagin duality, between compact and discrete commutative topologic ...
*
Krein–Milman theorem
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs).
This theorem generalizes to infinite-dimensional spaces and to arbitrar ...
and
Krein–Rutman theorem In functional analysis, the Krein–Rutman theorem is a generalisation of the Perron–Frobenius theorem to infinite-dimensional Banach spaces. It was proved by Krein and Rutman in 1948.
Statement
Let X be a Banach space, and let K\subset X ...
in
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...
*
Krein space In mathematics, in the field of functional analysis, an indefinite inner product space
:(K, \langle \cdot,\,\cdot \rangle, J)
is an infinite-dimensional complex vector space K equipped with both an indefinite inner product
:\langle \cdot,\,\cdo ...
*
Krein's condition In mathematical analysis, Krein's condition provides a necessary and sufficient condition for exponential sums
: \left\,
to be dense in a weighted L2 space on the real line. It was discovered by Mark Krein in the 1940s. A corollary, also called K ...
for the indeterminacy of the
problem of moments
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure ''μ'' to the sequences of moments
:m_n = \int_^\infty x^n \,d\mu(x)\,.
More generally, one may consider
:m_n = \int_^\infty M_n(x) ...
External links
*
*
INTERNATIONAL CONFERENCE Modern Analysis and Applications (MAA 2007). Dedicated to the centenary of Mark Krein*
{{DEFAULTSORT:Krein, Mark G.
1907 births
1989 deaths
Soviet mathematicians
Ukrainian Jews
Scientists from Kyiv
Wolf Prize in Mathematics laureates
Operator theorists
Functional analysts
Foreign associates of the National Academy of Sciences