Abstract
This paper recalls the work of D. Pompeiu who introduced the notion of set distance in his thesis published one century ago. The notion was further studied by F. Hausdorff, C. Kuratowski who acknowledged in their books the contribution of Pompeiu and it is frequently called the Hausdorff distance.
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G. Andonie. Istoria Matematicii in Romania. Ed. Ştiinţifică, Bucharest, 1965.
C.A. Bernstein. An inverse spectral theorem and its relation to the Pompeiu problem. J. d’Analyse Math. 37:128–144, 1980.
M. Fréchet. Sur quelques points du calcul fonctionnel (Thèse). Rend. Circ. Mat. Palermo. 22:1–74, 1906.
N. Garofalo, F. Segala. Univalent functions and the Pompeiu problem. Trans. A.M.S. 346:137–146, 1994.
F. Hausdorff. Grundzuege der Mengenlehre. Viet, Leipzig, 1914.
F. Hausdorff. Mengenlehre. Walter de Gruyter, Berlin, 1927.
C. Kuratowski. Topologie I. Polish Math. Soc., Warsaw, 1952.
S. Marcus. Funcţiile lui Pompeiu. Studii şi Cerc. Mat. 5:413–419, 1954.
M. Mitrea, F. Şabac. Pompeiu’s integral representation formula. History and mathematics. Rev.Roum.Math.Pures Appl. 43:211–226, 1998.
B.L. McAllister. Hyperspaces and multifunctions, the first halfcentury (1900–1950). Nieuw Arch. Wish. 26:309–329, 1978.
P. Neittaanmaki, J. Sprekels, D. Tiba. Optimization of elliptic systems. Theory and applications. Springer Verlag, New York, 2005.
O. Onicescu. Pe drumurile vieţii. Ed. Şt. şi Enciclopedică, Bucharest, 1981.
P. Painlevé. Leçons sur la théorie analytique des équations differentielles, professées a Stockholm. Hermann, Paris, 1897.
D. Pompeiu. Sur la continuité des fonctions de variables complexes (Thèse). Gauthier-Villars, Paris, 1905; Ann.Fac.Sci.de Toulouse 7:264–315, 1905.
D. Pompeiu. Opera Matematică. Ed.Acad.Române, Bucharest, 1959.
D. Pompeiu. Sur les fonctions derivées. Math.Ann. 63:326–332, 1907.
D. Pompeiu. Sur certains systemes d’equations linéires et sur une propriété intégrate des fonctions de plusieurs variables. C.R.Acad.Sc.Paris. 188:1138–1139, 1929.
M. Vogelius. An inverse problem for the equation Δu = −cu − d. Annales de I’Institut Fourier. 44:1181–1209, 1994.
S.A. Williams. A partial solution of the Pompeiu problem. Math. Ann. 223, 183–190, 1976.
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Birsan, T., Tiba, D. (2006). One Hundred Years Since the Introduction of the Set Distance by Dimitrie Pompeiu. In: Ceragioli, F., Dontchev, A., Futura, H., Marti, K., Pandolfi, L. (eds) System Modeling and Optimization. CSMO 2005. IFIP International Federation for Information Processing, vol 199. Springer, Boston, MA. https://doi.org/10.1007/0-387-33006-2_4
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DOI: https://doi.org/10.1007/0-387-33006-2_4
Publisher Name: Springer, Boston, MA
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