Alexander Ostrowski
Alexander Markovich Ostrowski (Russian Александр Маркович Островский, scientific transliteration Aleksandr Ostrovsky Markovič; born September 25, 1893 in Kiev, † November 20, 1986 in Montagnola near Lugano ) was a Russian- German -Swiss mathematician.
Life
Ostrowski's father was a merchant in Kiev. Alexander Ostrowski attended the trade school, but has also played already as a 15 -year-old mathematical seminar at the University of Kiev under Dmitri Alexandrovich Grawe equal footing and also wrote his first publication. Since he had just graduated from the trade school, he was able to study despite Grawes intercede only in Germany, where he was accepted by Kurt Hensel at the University of Marburg in 1912 as a student. During his internment during World War I he was on Hensel's intercession continue to use the library and was able to concentrate on mathematics.
In 1918 he resumed his studies at the University of Göttingen with David Hilbert and Edmund Landau back on and received his doctorate 1920. Afterwards he was with Erich Hecke, University of Hamburg, where he habilitated in 1922. From 1923 to 1927 he taught as a Privatdozent in Göttingen. In the years 1925 and 1926 he was a scholarship from the Rockefeller Foundation in England.
1927 Ostrowski was appointed to a full professorship at the University of Basel. In 1950, he acquired Swiss citizenship in Basel. After his retirement in 1958 he continued to teach as a visiting professor at various universities in the U.S. and was also associated as a numerical analyst with the National Bureau of Standards of the United States.
Work
Ostrowski has delivered on many areas of mathematics, important contributions, but especially in the analysis. In 1920 he proved that Dirichlet series whose coefficients can not be expressed by a finite basis, satisfy any algebraic differential equation, where he released an upside- Hilbert problem ( Hilbert treated the case of the Riemann zeta function).
Two different basic facts from valuation theory or the theory of the amounts are often referred to as a set of Ostrowski:
- The only possible sum functions of the rational numbers (up to equivalence ) the trivial amount that the real absolute value and the standard p-adic amounts primes p. Because of the relationship between amounts and ratings are thus all reviews on known, which in turn helps to classify the reviews of specific body enhancements.
- Every body that is complete with respect to an archimedean amount is algebraically and topologically isomorphic to the field of real numbers or the field of complex numbers. In other words, there is no real field extension of complex numbers, the absolute value of the complex can be continued. A generalization of this theorem for complex Banach algebras is the set of Gelfand - Mazur.
Ostrowski has been instrumental in the field of numerical analysis and provided many accurate evidence of the convergence of different methods. He also developed many, even today used in the numerical analysis, a stable process. He also worked a lot in the numerical linear algebra.
Named after him Ostrowski Prize is awarded for outstanding achievements in mathematics since 1989.
Writings
- Collected mathematical papers, 5 vols, Birkhäuser, Basel, 1983-1984
- Collection of problems in Calculus, several vols, Birkhauser, 1972 ( first 1964)
- Lectures on Differential and Integral Calculus, 3 vols, Birkhauser, 2nd ed. 1963 ( first 1945, 1951)
- Solution of equations and systems of equations, Academic Press 1960, 1965