Dimitrie Pompeiu

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Dimitrie Pompeiu (born September 22 . Jul / 4. October  1873 greg. In Brosca in Dorohoi ; † 8. October 1954 in Bucharest ) was a Romanian mathematician.

Life

Pompeiu studied at the University of Education in Bucharest with the degree in 1893. He then taught Galati and Ploiest. In 1898 he continued his mathematics studies in Paris and received his doctorate in 1905 under Henri Poincaré (Sur la continuité des fonctions de variable complexes). After returning to Romania he became a professor in Iași . In 1912 he became professor of mechanics in Bucharest as the successor to Spiru Haret . In 1930 he moved to the chair for function theory as the successor to David Emmanuel .

Pompey was primarily concerned with analysis. In his dissertation he later introduced Pompei functions named after him , which are differentiable everywhere, but whose derivative vanishes on one dense set and is discontinuous on another dense set. In his dissertation he also introduced a distance that later became known as the Hausdorff distance ( Felix Hausdorff referred to Pompeiu in his book on set theory in 1914).

The Pompeiu problem has its origin in an essay by Pompeiu in 1929 and was the starting point for numerous researches. In its original form the problem is: does a continuous function vanish identically in two variables if its integral vanishes over all disks of fixed radius? In general, one speaks of a domain in the real plane having the Pompeiu property if the function f = 0, which is identical everywhere, is the only continuous function with the property that its area integral on domain G and domains resulting from G by a any rigid movement emerges disappears. The Pompeiu problem is the conjecture that the circular disk is the only bounded simply connected area of ​​the real plane for which the Pompeiu property does not apply.

The Möbius-Pompeiu theorem is named after him , which states that the distances of a point P from the corners of an equilateral triangle , in whose plane P lies, form the side lengths of a triangle.

In 1934 he became a member of the Romanian Academy of Sciences.

literature

  • BJ Malešević: The Möbius-Pompeiu Metric Property . arxiv : math / 0409289 (English)
    Proof of a generalization of the Möbius-Pompeiu theorem to certain metric spaces
  • D. Mitrinović, J. Pečarić, J., V. Volenec: History, Variations and Generalizations of the Möbius-Neuberg theorem and the Möbius-Ponpeiu . In: Bulletin Mathématique De La Société Des Sciences Mathématiques De La République Socialiste De Roumanie , 31 (79), No. 1, 1987, pp. 25-38 ( JSTOR 43681294 )

Web links

Individual evidence

  1. ↑ Pompeiu Sur les fonctions dérivées . In: Mathematische Annalen , 63, 1907, pp. 326-332
  2. ↑ Pompeiu Sur certains systèmes d'équations linéaires et sur une propriété intégrale des fonctions de plusieurs variables . In: Comptes Rendus de l'Académie des Sciences . Série I. Mathématique, Volume 188, 1929, pp. 1138-1139
  3. ^ Carlos Berenstein: Pompeiu problem . Encyclopedia of Mathematics
  4. ^ Mathworld
personal data
SURNAME Pompey, Dimitrie
BRIEF DESCRIPTION Romanian mathematician
DATE OF BIRTH October 4, 1873
PLACE OF BIRTH Brosca , near Dorohoi , Romania
DATE OF DEATH October 8, 1954
Place of death Bucharest , Romania