Alfred Pringsheim

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Alfred Pringsheim bigraphy, stories - Mathematicians

Alfred Pringsheim : biography

2 September 1850 – 25 June 1941

Alfred Pringsheim (2 September 1850 – 25 June 1941) was a German mathematician and patron of the arts. He was born in Ohlau, Prussian Silesia (now Oława, Poland) and died in Zürich, Switzerland. One of many antisemitic pieces of Nazi legislation, the which came into effect 1 January 1938, forced him to legally change his name into Alfred Israel Pringsheim at age 87.

Literature

  • Inge und Walter Jens: Auf der Suche nach dem verlorenen Sohn – Die Südamerika-Reise der Hedwig Pringsheim 1907/8. Rowohlt Verlag, Reinbek, 2006, ISBN 3-498-05304-3
  • Lorenz Seelig: Die Münchner Sammlung Alfred Pringsheim – Versteigerung, Beschlagnahmung, Restitution. In: Entehrt. Ausgeplündert. Arisiert. Entrechtung und Enteignung der Juden, bearb. von Andrea Baresel-Brand (= Veröffentlichungen der Koordinierungsstelle für Kulturgutverluste, Bd. 3). Magdeburg 2005, pp. 265–290. ISBN 3-00-017002-2
  • Inge und Walter Jens: Katias Mutter. Das außerordentliche Leben der Hedwig Pringsheim. Rowohlt. Reinbek, 2005. ISBN 3-498-03337-9
  • Katia Mann: Meine ungeschriebenen Memoiren. Fischer TB. Frankfurt, 2000. ISBN 3-596-14673-9
  • Inge und Walter Jens: Frau Thomas Mann. Das Leben der Katharina Pringsheim. Rowohlt. Reinbek, 2003. ISBN 3-498-03338-7
  • Kirsten Jüngling/Brigitte Roßbeck: Katia Mann. Die Frau des Zauberers. Brigitte Propyläen. 2003. ISBN 3-549-07191-4

Sources

  • Ernst Klee, Das Kulturlexikon zum Dritten Reich, Frankfurt/Main 2007
  • Franz Neubert (Hrsg.), Deutsches Zeitgenossen-Lexikon, Leipzig 1905
  • Hermann A.L. Degener, Wer ist’s, Leipzig 1911
  • Hermann A.L. Degener, Wer ist’s, Berlin 1935
  • Tilmann Lahme, "Von der Wand in den Mund – Ordnung und spätes Leid im Haus der Schwiegereltern Thomas Manns: Die Pringsheims im Münchner Jüdischen Museum", artikel in the Frankfurter Allgemeine Zeitung dated 7 April 2007

Mathematical investigations

In mathematical analysis, Pringsheim studied real and complex functions, following the power-series-approach of the Weierstrass school. Pringsheim published numerous works on the subject of complex analysis, with a focus on the summability theory of infinite series and the boundary behavior of analytic functions.

One of Pringsheim’s theorems, according to Hadamard earlier proved by E. Borel, states that a power series with positive coefficients and radius of convergence equal to 1 has necessarily a singularity at the point 1. This theorem is used in analytic combinatoricsPhilippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge University Press, 2008, ISBN 0-521-89806-4 and the Perron–Frobenius theory of positive operators on ordered vector spacesSamuel Karlin and H. M. Taylor. "A First Course in Stochastic Processes." Academic Press, 1975 (second edition). Samuel Karlin. "Mathematical Methods and Theory in Games, Programming, and Economics." Dover Publications, 1992. ISBN 978-0-486-67020-1.

Another theorem called after Pringsheim gives an analyticity criterium for a C∞ function on a bounded interval, based on the behaviour of the radius of convergence of the Taylor expansion around a point of the interval. However, Pringsheim’s original proof had a flaw (related to uniform convergence), and a correct proof was provided by Ralph P. Boas.

Pringsheim and Ivan Śleszyński, working separately, proved what is now called the Śleszyński–Pringsheim theorem on convergence of certain continued fractions.

Besides his research in analysis, Pringsheim also wrote articles for the Enzyklopädie der mathematischen Wissenschaften on the fundamentals of arithmetic and on number theory. He published papers in the Mathematische Annalen. As an officer of the Bayerische Akademie der Wissenschaften, he recorded the minutes of its scientific meetings.

Family and academic career