Jovan Karamata
Encyclopedia
Jovan Karamata was one of the greatest Serbia
n mathematicians of the 20th century. He is remembered for contributions to analysis
, in particular, the Tauberian theory
and the theory of slowly varying function
s. Karamata was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts
in 1946.
on February 1, 1902 in an ethnic Serb
family descending from a merchant family from the city of Zemun
in Serbia
. His family's business affairs on the borders of the Austro-Hungarian and Ottoman
empires were very well known. In 1914, he finished most of his primary school in Zemun but because of constant warfare on the borderlands, Karamata's father sent him, together with his brothers and his sister, to Switzerland
for their own safety. In Lausanne
, 1920, he finished primary school oriented towards mathematics and sciences. In the same year he enrolled at the Engineering faculty of Belgrade University and, after several years moved to the Philosophy and Mathematicians sector, where he graduated in 1925.
He spent the years 1927–1928 in Paris
, as a fellow of the Rockefeller Foundation
, and in 1928 he became Assistant for Mathematics at the Faculty of Philosophy of Belgrade University. In 1930 he became Assistant Professor, in 1937 Associate Professor and, after the end of World War II
, in 1950 he became Full Professor. In 1951 he was elected Full Professor at the University of Geneva
. In 1933 he became a member of Yugoslav Academy of Sciences and Arts
, Czech Royal Society in 1936, and Serbian Royal Academy in 1939 as well as a fellow of Serbian Academy of Sciences in 1948. He was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts
in 1946.
Karamata was member of the Swiss, French
and German
mathematical societies, the French Association for the Development of Science, and the primary editor of the journal L’Enseignement Mathématique in Geneva
. He also taught at the University of Novi Sad
.
In 1931 he married Emilija Nikolajevic, who gave birth to their two sons and a daughter. His wife died in 1959. After a long illness, Karamata died on August 14, 1967 in Geneva. His ashes rest in his native town of Zemun.
Karamata is best known for his work on mathematical analysis
. He introduced the notion of regularly varying function, and discovered a new class of theorems of Tauberian type, today known as Karamata's tauberian theorems. He also worked on Mercer's theorem
s, Froullani’s integrals, and other topics in analysis. In 1935 he introduced the brackets and braces notation for Stirling numbers (analogous to the binomial coefficients notation), which is now known as Karamata notation. He is also cited for Karamata's inequality
.
In Serbia, Karamata founded the "Karamata's (Yugoslav) school of mathematics”. Today, Karamata is the most frequently cited Serbian mathematician. He is the developer and co-developer of dozens of mathematical theorems and has a lasting influence in 20th century mathematics.
Serbia
Serbia , officially the Republic of Serbia , is a landlocked country located at the crossroads of Central and Southeast Europe, covering the southern part of the Carpathian basin and the central part of the Balkans...
n mathematicians of the 20th century. He is remembered for contributions to analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, in particular, the Tauberian theory
Abelian and tauberian theorems
In mathematics, abelian and tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber...
and the theory of slowly varying function
Slowly varying function
In real analysis, a branch of mathematics, a slowly varying function is a function resembling a function converging at infinity. A regularly varying function resembles a power law function near infinity...
s. Karamata was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts
Serbian Academy of Sciences and Arts
The Serbian Academy of Sciences and Arts is the most prominent academic institution in Serbia today...
in 1946.
Life
Jovan Karamata was born in ZagrebZagreb
Zagreb is the capital and the largest city of the Republic of Croatia. It is in the northwest of the country, along the Sava river, at the southern slopes of the Medvednica mountain. Zagreb lies at an elevation of approximately above sea level. According to the last official census, Zagreb's city...
on February 1, 1902 in an ethnic Serb
Serbs
The Serbs are a South Slavic ethnic group of the Balkans and southern Central Europe. Serbs are located mainly in Serbia, Montenegro and Bosnia and Herzegovina, and form a sizable minority in Croatia, the Republic of Macedonia and Slovenia. Likewise, Serbs are an officially recognized minority in...
family descending from a merchant family from the city of Zemun
Zemun
Zemun is a historical town and one of the 17 municipalities which constitute the City of Belgrade, the capital of Serbia...
in Serbia
Serbia
Serbia , officially the Republic of Serbia , is a landlocked country located at the crossroads of Central and Southeast Europe, covering the southern part of the Carpathian basin and the central part of the Balkans...
. His family's business affairs on the borders of the Austro-Hungarian and Ottoman
Ottoman Empire
The Ottoman EmpireIt was usually referred to as the "Ottoman Empire", the "Turkish Empire", the "Ottoman Caliphate" or more commonly "Turkey" by its contemporaries...
empires were very well known. In 1914, he finished most of his primary school in Zemun but because of constant warfare on the borderlands, Karamata's father sent him, together with his brothers and his sister, to Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
for their own safety. In Lausanne
Lausanne
Lausanne is a city in Romandy, the French-speaking part of Switzerland, and is the capital of the canton of Vaud. The seat of the district of Lausanne, the city is situated on the shores of Lake Geneva . It faces the French town of Évian-les-Bains, with the Jura mountains to its north-west...
, 1920, he finished primary school oriented towards mathematics and sciences. In the same year he enrolled at the Engineering faculty of Belgrade University and, after several years moved to the Philosophy and Mathematicians sector, where he graduated in 1925.
He spent the years 1927–1928 in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, as a fellow of the Rockefeller Foundation
Rockefeller Foundation
The Rockefeller Foundation is a prominent philanthropic organization and private foundation based at 420 Fifth Avenue, New York City. The preeminent institution established by the six-generation Rockefeller family, it was founded by John D. Rockefeller , along with his son John D. Rockefeller, Jr...
, and in 1928 he became Assistant for Mathematics at the Faculty of Philosophy of Belgrade University. In 1930 he became Assistant Professor, in 1937 Associate Professor and, after the end of World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, in 1950 he became Full Professor. In 1951 he was elected Full Professor at the University of Geneva
University of Geneva
The University of Geneva is a public research university located in Geneva, Switzerland.It was founded in 1559 by John Calvin, as a theological seminary and law school. It remained focused on theology until the 17th century, when it became a center for Enlightenment scholarship. In 1873, it...
. In 1933 he became a member of Yugoslav Academy of Sciences and Arts
Croatian Academy of Sciences and Arts
The Croatian Academy of Sciences and Arts is the national academy of Croatia. It was founded in 1866 as the Yugoslav Academy of Sciences and Arts , and was known by that name for most of its existence.- History :...
, Czech Royal Society in 1936, and Serbian Royal Academy in 1939 as well as a fellow of Serbian Academy of Sciences in 1948. He was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts
Serbian Academy of Sciences and Arts
The Serbian Academy of Sciences and Arts is the most prominent academic institution in Serbia today...
in 1946.
Karamata was member of the Swiss, French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
and German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematical societies, the French Association for the Development of Science, and the primary editor of the journal L’Enseignement Mathématique in Geneva
Geneva
Geneva In the national languages of Switzerland the city is known as Genf , Ginevra and Genevra is the second-most-populous city in Switzerland and is the most populous city of Romandie, the French-speaking part of Switzerland...
. He also taught at the University of Novi Sad
University of Novi Sad
The University of Novi Sad is a university located in Novi Sad, the capital of Serbian province of Vojvodina and the second largest city in Serbia....
.
In 1931 he married Emilija Nikolajevic, who gave birth to their two sons and a daughter. His wife died in 1959. After a long illness, Karamata died on August 14, 1967 in Geneva. His ashes rest in his native town of Zemun.
Legacy
Karamata published 122 scientific papers, 15 monographs and text-books as well as 7 professional-pedagogical papers.Karamata is best known for his work on mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
. He introduced the notion of regularly varying function, and discovered a new class of theorems of Tauberian type, today known as Karamata's tauberian theorems. He also worked on Mercer's theorem
Mercer's theorem
In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in , is one of the most notable results of the work of James Mercer...
s, Froullani’s integrals, and other topics in analysis. In 1935 he introduced the brackets and braces notation for Stirling numbers (analogous to the binomial coefficients notation), which is now known as Karamata notation. He is also cited for Karamata's inequality
Karamata's inequality
In mathematics, Karamata's inequality, named after Jovan Karamata, also known as the majorization inequality, is a theorem in elementary algebra for convex and concave real-valued functions, defined on an interval of the real line...
.
In Serbia, Karamata founded the "Karamata's (Yugoslav) school of mathematics”. Today, Karamata is the most frequently cited Serbian mathematician. He is the developer and co-developer of dozens of mathematical theorems and has a lasting influence in 20th century mathematics.
Further reading
- N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, vol. 27, Cambridge Univ. Press, 1987.
- J.L. Geluk, L. de Haan, Regular Variation Extensions and Tauberian Theorems, CWI Tract 40, Amsterdam, 1987.
- Maric V, Radasin Z, Regularly Varying Functions in Asymptotic Analysis
- Nikolic A, About two famous results of Jovan Karamata, Archives Internationales d’Histoire des Sciences
- Nikolic A, Jovan Karamata (1902–1967), Lives and work of the Serbian scientists, SANU, Biographies and bibliographies, Book 5
- Tomic M, Academician Jovan Karamata, on occasion of his death, SANU, Vol CDXXIII, t. 37, Belgrade, 1968 (in Serbian)
- Tomic M, Jovan Karamata (1902–1967), L’Enseignement Mathématique
- Tomic M, Aljancic S, Remembering Karamata, Publications de l’Institut Mathématique