Dimitrie Pompeiu

Dimitrie Pompeiu (born 22 Septemberjul / October 4 1873greg in Brosca in Dorohoi, .. † October 8, 1954 in Bucharest ) was a Romanian mathematician.

Life

Pompeiu studied at the Pedagogical University in Bucharest with the conclusion of 1893. Afterwards he taught Galati and Ploiest. In 1898 he continued his studies in Paris and mathematics continued in 1905 with Henri Poincaré doctorate ( Sur la continuite des fonctions de variables complexes ). After returning to Romania, he became a professor in Iasi. In 1912 he became professor of mechanics in Bucharest as the successor of Spiru Haret. In 1930 he moved to the Chair of Function Theory, succeeding David Emmanuel.

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

The Pompeiu problem has its origin in a paper by Pompeiu 1929 and was the starting point for numerous investigations. In its original form is the problem disappears a continuous function in two variables are identical if their integral vanishes over all disks of fixed radius? Generally one speaks of them, have an area in the real plane the Pompeiu property, if the same everywhere vanishing function f = 0 the only continuous function with the property is the one you surface integral on the domain G and territories through from G any rigid motion emerge, disappear. The Pompeiu problem is the assumption, which is the circular disk the only limited simply connected region of the real plane, for which the Pompeiu property does not apply.

Named after him is the set of Möbius Pompeiu, which states that the distances of a point P in the plane P is of the corners of an equilateral triangle, where the side lengths of a triangle.

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