Jovan Karamata

Memorial plaque of Jovan Karamata in Zemun

Jovan Karamata ( Serbian - Cyrillic Јован Карамата ; born February 1, 1902 in Zagreb , † August 14, 1967 in Geneva ) was a Yugoslav mathematician who made contributions to analysis , especially the theory of slowly varying functions.

Life

Karamata first grew up in Zemun . When the First World War broke out in 1914, his father sent him and his siblings to Switzerland, where he attended a mathematics and science high school in Lausanne . From 1920 to 1922 he studied at the technical faculty of the University of Belgrade , then switched to the mathematics department of the philosophical faculty and graduated in 1925. Three months later he submitted his doctoral thesis, in 1926 he received his doctorate under Mihailo Petrović ( O jednoj vrsti granica sličnih određenim integralima ). He spent the years 1927 and 1928 in Paris on a Rockefeller scholarship, after which he became an assistant for mathematics at the University of Belgrade. In 1930 he became a lecturer there, in 1937 an associate professor and in 1950 a full professor, in 1951 he was appointed to the University of Geneva , where he remained until his death.

In 1930 Karamata showed that a positive continuous function on the positive real numbers is then slowly varying, i.e. the condition for all ${\displaystyle L}$ ${\displaystyle t>0}$

${\displaystyle L(t\,x)/L(x)\to 1}$     For     ${\displaystyle x\to \infty }$

met when for one for in shape ${\displaystyle a>0}$ ${\displaystyle x>a}$

${\displaystyle L(x)=c(x)\exp \int _{a}^{x}\!\varepsilon (t)/t\ dt}$     with         and         for     ${\displaystyle c(x)\to c>0}$ ${\displaystyle \varepsilon (x)\to 0}$ ${\displaystyle x\to \infty }$

can be written.

His PhD students included Vojislav Avakumović, Slobodan Aljančić, Ranko Bojanic, and Ronald Coifman .

Fonts

• Sur un mode de croissance régulière des fonctions , Mathematica (Cluj) 4, 1930, pp. 38–53 (French)
• On the Hardy-Littlewood inversions of Abel's continuity theorem (March 12, 1930), Mathematische Zeitschrift 32, December 1930, pp. 319-320
• Sur un mode de croissance régulière. Théorèmes fondamentaux , Bulletin de la Société Mathématique de France 61, 1933, pp. 55–62 (French)
• Sur les théorèmes inverses des procédés de sommabilité , Hermann, Paris 1937 (French)

literature

• Miodrag Tomić: Jovan Karamata (1902–1967) , L'Enseignement Mathématique 15, 1969, pp. 1–20 (French; obituary; with list of writings)
• Miodrag Tomić, Slobodan Aljančić: Remembering Jovan Karamata ( PDF file, 423 kB), Publications de l'Institut Mathématique Nouvelle série 48, 1990, pp. 1–6 (English)
• Miodrag Tomić: Jovan Karamata 1902–1967 , Bulletin de l'Académie Serbe des Sciences et des Arts 122, 2001, pp. 1–29 (English; with list of writings)
• Aleksandar Nikolić: Jovan Karamata (1902–1967) ( PDF file, 152 kB), Novi Sad Journal of Mathematics 32, 2002, pp. 1–5 (English)
• Vojislav Marić: Jovan Karamata (1902–1967) , Matematichki Vesnik 54, 2002, pp. 45–51 (English)

Web links

• Jovan Karamata (1902 - 1967) from Aleksandar Nikolić at the Mathematical Institute of the SANU (English; with picture)