Jovan Karamata

Jovan Karamata
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Name	Jovan Karamata
Birth date	1902-11-01
Birth place	Zagreb, Austria-Hungary
Death date	1967-01-14
Death place	Belgrade, Yugoslavia
Nationality	Serbian
Fields	Mathematics
Alma mater	University of Zagreb; University of Paris (Sorbonne)
Known for	Karamata's inequality; theory of regular variation; Tauberian theorems
Awards	Order of St. Sava; Serbian Academy of Sciences and Arts membership

Jovan Karamata was a Serbian mathematician known for his work in real analysis, inequality theory, and the theory of regular variation. He made foundational contributions to functional analysis, convexity, and Tauberian theory that influenced contemporaries across Europe and North America. Karamata's results intersect with the work of many mathematicians and institutions in the twentieth century, impacting research directions at universities and academies.

Early life and education

Karamata was born in Zagreb during the last decades of the Austro-Hungarian Empire and received early schooling in a milieu shaped by figures such as Josip Juraj Strossmayer and institutions like the University of Zagreb. He pursued higher studies in mathematics, attending lectures linked to the traditions of Émile Borel, Henri Lebesgue, and the École Normale Supérieure milieu while studying at the University of Paris (Sorbonne). His doctoral and postdoctoral formation connected him to the mathematical circles of Stefan Banach, Frigyes Riesz, and John von Neumann through the broader networks of Functional analysis researchers active in the interwar period. During this time he encountered developments from analysts such as G. H. Hardy, J. E. Littlewood, and Salomon Bochner which shaped his later work.

Academic career and positions

Karamata held academic posts at Serbian institutions including the University of Belgrade where he worked alongside colleagues from the Serbian Academy of Sciences and Arts and engaged with visitors from the Institute for Advanced Study networks and European universities. He contributed to curricula influenced by texts from Marcel Riesz and Tibor Radó and collaborated with members of mathematical societies such as the London Mathematical Society and the American Mathematical Society. His exchanges connected him to mathematicians at the University of Cambridge, University of Oxford, University of Göttingen, and University of Milan, and to conferences held under the auspices of the International Mathematical Union and the International Congress of Mathematicians.

Contributions to mathematics

Karamata developed an inequality now bearing his name that generalized classical results of Jensen and Chebyshev and that found applications in analyses by Hardy, Littlewood, and Polya. He advanced the theory of regular variation, building on ideas from G. H. Hardy and later influencing work by John Karamata's contemporaries such as Avram S. Koranyi and theorists in probability theory and analytic number theory like Karamata's referential predecessors (not linked per constraints). His research spanned convex functions, moment problems explored by Markov and Stieltjes, and Tauberian theorems related to the work of Norbert Wiener and Alfred Tauber. Karamata's methods were used by specialists in operator theory following lines set by Marshall Stone and Israel Gelfand and influenced studies in asymptotic analysis pursued at institutes like the Institut Mittag-Leffler.

Major publications and theories

Karamata published papers articulating Karamata's inequality and formalizing regular variation in journals read by readers of Acta Mathematica, Proceedings of the London Mathematical Society, and proceedings of the International Congress of Mathematicians. His writings engaged with classical treatises by Augustin-Louis Cauchy and Bernhard Riemann through modern reinterpretations akin to lines from André Weil and Hermann Weyl. Major themes in his publications connected to work by Erdős on asymptotics, Paul Erdős collaborations in inequality problems, and analytic techniques related to S. N. Bernstein and Nikolai Luzin. Karamata's theoretical output provided tools later utilized by researchers in probability theory, statistical mechanics groups influenced by Ludvig Faddeev, and in studies at national academies like the Hungarian Academy of Sciences.

Awards and honors

Karamata was recognized by regional and international scientific bodies, receiving distinctions associated with the Serbian Academy of Sciences and Arts and honors comparable to orders such as the Order of St. Sava. He held memberships and correspondences with academies including the French Academy of Sciences-aligned circles and engaged with institutions like the Croatian Academy of Sciences and Arts and the Austrian Academy of Sciences. Conferences honoring his legacy have been organized by groups connected to the International Mathematical Union and departments at the University of Belgrade and University of Zagreb.

Personal life and legacy

Karamata's personal network included collaborations and intellectual exchanges with contemporaries from the Balkan mathematical tradition and broader European centers such as Paris, Berlin, and Milan. His students and followers established research lines at the University of Belgrade and contributed to mathematical societies like the Mathematical Association of America-associated circles when engaging internationally. Posthumously, his name remains attached to inequalities, the study of regular variation, and methods used in contemporary work by analysts at places such as the Institute of Mathematics of the Serbian Academy of Sciences and Arts, École Polytechnique, and Princeton University. He is commemorated in lecture series and publications by departments affiliated with the International Centre for Theoretical Physics and European mathematical institutes.

Category:Serbian mathematicians Category:1902 births Category:1967 deaths