4 October 1873|
Broscǎuţi, Romanian Principalities
|Died||8 October 1954
Bucharest, Romanian People's Republic
|Institutions||University of Iaşi
University of Bucharest
|Alma mater||University of Bucharest|
|Doctoral advisor||Henri Poincaré|
|Doctoral students||Grigore Moisil|
|Known for||Cauchy–Pompeiu formula
After studying in Dorohoi and Bucharest, he went to France, where he studied mathematics at the University of Paris (the Sorbonne). He obtained a Ph.D. degree in mathematics in 1905 with a thesis, On the continuity of complex variable functions, written under the direction of Henri Poincaré. After returning to Romania, he was named Professor of Mechanics at the University of Iaşi. In 1912, he assumed a chair at the University of Bucharest. In 1934, he was elected member of the Romanian Academy.
His contributions were mainly in the field of mathematical analysis, complex functions theory, and rational mechanics. In an article published in 1929, he posed a challenging conjecture in integral geometry, now widely known as the Pompeiu problem. Among his contributions to real analysis there is the construction, dated 1906, of non-constant, everywhere differentiable functions, with derivative vanishing on a dense set. Such derivatives are now called Pompeiu derivatives.
- Pompeiu, D. (1905), "Sur la continuité des fonctions de variables complexes", Annales de la faculté des sciences de Toulouse, Série 2 (in French) 7 (3): 265–315, JFM 36.0454.04.
- Pompeiu, D. (1912), "Sur une classe de fonctions d'une variable complexe", Rendiconti del Circolo Matematico di Palermo (in French) 33 (1): 108–113, doi:10.1007/BF03015292, JFM 43.0481.01.
- Pompeiu, D. (1913), "Sur une classe de fonctions d'une variable complexe et sur certaines équations intégrales", Rendiconti del Circolo Matematico di Palermo (in French) 35 (1): 277–281, doi:10.1007/BF03015607.
- Cauchy–Pompeiu formula
- Pompeiu–Hausdorff metric
- Pompeiu's theorem
- Pompeiu derivative
- Wirtinger derivatives
- Short biography of Dimitrie Pompeiu, National Institute for R&D in Informatics
- One hundred years since the introduction of the set distance by Dimitrie Pompeiu, by T. Bârsan and D. Tiba, Institute of Mathematics of the Romanian Academy
- Short biography of Dimitrie Pompeiu, by Petre Mocanu, Babeş–Bolyai University
- Fichera, Gaetano (1969), "Derivata areolare e funzioni a variazione limitata", Revue Roumaine de Mathématiques Pures et Appliquées (in Italian) XIV (1): 27–37, MR 0265616, Zbl 0201.10002. "Areolar derivative and functions of bounded variation" is an important reference paper in the theory of areolar derivatives.
- Henrici, Peter (1993) , Applied and Computational Complex Analysis Volume 3, Wiley Classics Library (Reprint ed.), New York–Chichester–Brisbane–Toronto–Singapore: John Wiley & Sons, pp. X+637, ISBN 0-471-58986-1, MR 0822470, Zbl 1107.30300.