One Hundred Years Since the Introduction of the Set Distance by Dimitrie Pompeiu

  • T. Birsan
  • D. Tiba
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 199)

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.

keywords

Hausdorff distance Hausdorff-Pompeiu distance Pompeiu functions Pompeiu conjecture Schiffer conjecture 

References

  1. [1]
    G. Andonie. Istoria Matematicii in Romania. Ed. Ştiinţifică, Bucharest, 1965.Google Scholar
  2. [2]
    C.A. Bernstein. An inverse spectral theorem and its relation to the Pompeiu problem. J. d’Analyse Math. 37:128–144, 1980.Google Scholar
  3. [3]
    M. Fréchet. Sur quelques points du calcul fonctionnel (Thèse). Rend. Circ. Mat. Palermo. 22:1–74, 1906.MATHCrossRefGoogle Scholar
  4. [4]
    N. Garofalo, F. Segala. Univalent functions and the Pompeiu problem. Trans. A.M.S. 346:137–146, 1994.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    F. Hausdorff. Grundzuege der Mengenlehre. Viet, Leipzig, 1914.MATHGoogle Scholar
  6. [6]
    F. Hausdorff. Mengenlehre. Walter de Gruyter, Berlin, 1927.MATHGoogle Scholar
  7. [7]
    C. Kuratowski. Topologie I. Polish Math. Soc., Warsaw, 1952.MATHGoogle Scholar
  8. [8]
    S. Marcus. Funcţiile lui Pompeiu. Studii şi Cerc. Mat. 5:413–419, 1954.MATHGoogle Scholar
  9. [9]
    M. Mitrea, F. Şabac. Pompeiu’s integral representation formula. History and mathematics. Rev.Roum.Math.Pures Appl. 43:211–226, 1998.MATHGoogle Scholar
  10. [10]
    B.L. McAllister. Hyperspaces and multifunctions, the first halfcentury (1900–1950). Nieuw Arch. Wish. 26:309–329, 1978.MATHMathSciNetGoogle Scholar
  11. [11]
    P. Neittaanmaki, J. Sprekels, D. Tiba. Optimization of elliptic systems. Theory and applications. Springer Verlag, New York, 2005.Google Scholar
  12. [12]
    O. Onicescu. Pe drumurile vieţii. Ed. Şt. şi Enciclopedică, Bucharest, 1981.Google Scholar
  13. [13]
    P. Painlevé. Leçons sur la théorie analytique des équations differentielles, professées a Stockholm. Hermann, Paris, 1897.Google Scholar
  14. [14]
    D. Pompeiu. Sur la continuité des fonctions de variables complexes (Thèse). Gauthier-Villars, Paris, 1905; Ann.Fac.Sci.de Toulouse 7:264–315, 1905.Google Scholar
  15. [15]
    D. Pompeiu. Opera Matematică. Ed.Acad.Române, Bucharest, 1959.MATHGoogle Scholar
  16. [16]
    D. Pompeiu. Sur les fonctions derivées. Math.Ann. 63:326–332, 1907.MATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    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.MATHGoogle Scholar
  18. [18]
    M. Vogelius. An inverse problem for the equation Δu = −cu − d. Annales de I’Institut Fourier. 44:1181–1209, 1994.MATHMathSciNetGoogle Scholar
  19. [19]
    S.A. Williams. A partial solution of the Pompeiu problem. Math. Ann. 223, 183–190, 1976.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • T. Birsan
    • 1
  • D. Tiba
    • 2
  1. 1.Department of Mathematics“Gh. Asachi” UniversityIasiRomania
  2. 2.Institute of MathematicsRomanian AcademyBucharestRomania

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