Sunday, October 4, 2009

Dimitrie Pompeiu (1873–1954)

Dimitrie Pompeiu (October 4, 1873, Broscǎuţi, Botoşani – October 8, 1954, Bucharest) - orthodox christian, and one of the greatest Romanian mathematicians. He is remembered in the mathematical world for numerous contributions such as: the set distance [1] that he introduced in his 1905 Université de Paris dissertation published in the same year in the Annales de la faculté des sciences de Toulouse (a set distance was introduced in a slightly different form in 1914 by Hausdorff, who credited Pompeiu's definition though), his contributions in complex analysis, including the areolar derivative [2] and the seminal Cauchy-Pompeiu's formula (higher dimensional analogues of the Cauchy-Pompeiu formula are topics of current research, while the formula was used in the theory of functions of several complex variables by Dolbeault and Grothendieck [5]), and for the celebrated Pompeiu's Conjecture that he formulated in his 1929 C. R. Acad. Sci. Paris article [4], a conjecture not fuly proved yet. Still, elegant analogues of Pompeiu's Conjecture continue to be proved in other areas [6] - this is an indicator of the fertility of the idea.


[1] T. Bârsan and D. Tiba. One hundred years since the introduction of the set distance by Dimitrie Pompeiu. Institute of Mathematics of the Romanian Academy.
[2] D. Pompeiu. Sur une classe de fonctions d'une variable complexe. Rendiconti del Circolo Matematico di Palermo, t. XXXIII, Ist sem. 1912, pp. 108-113.
[3] Pompeiu's biography from the The MacTutor History of Mathematics archive.
[4] D. Pompeiu. Sur certains systèmes d'équations linéaires et sur une propriété intégrale des fonctions de plusieurs variables, Comptes Rendus de l'Académie des Sciences Paris Série I. Mathématique, 188, 1138 –1139 (1929).
[5] R. Remmert. Theory of Complex Functions. Graduate Texts in Mathematics, Springer Verlag, 2nd Edition (1989).
[6] D. Zeilberger. Pompeiu's problem on Discrete Space. Proc. Natl. Acad. Sci. USA, Vol. 75 (8), 3555-3556 (1978).