Abstract

A reflection on the inceptive role of Moreau in various studies is presented. Gustave Choquet (1915-2006), Jean Jacques Moreau (1923-2014) and Ennio De Giorgi (1928-1996) inspired developments of variational analysis. I had the fortune to know them all and to follow their tracks

Author information

Contact details are reproduced from the original publication and may be historical.

References

  1. G. Choquet: Sur les notions de filtre et de grille, C. R. Acad. Sci., Paris 224 (1947) 171–173.Google Scholar
  2. G. Choquet: Convergences, Ann. Univ. Grenoble, Sect. Sci. Math. Phys., II. Ser. 23 (1948) 55–112.Google Scholar
  3. S. Dolecki: Continuity of bilinear and non bilinear polarities, in: Optimization and Related Fields (Erice, 1984), R. Conti et al. (ed.), Springer, Berlin (1986).https://doi.org/10.1007/BFb0076707Google Scholar
  4. S. Dolecki, G. H. Greco: Cyrtologies of convergences, I, Math. Nachr. 126 (1986) 327–348.https://doi.org/10.1002/mana.19861260122Google Scholar
  5. S. Dolecki, G. H. Greco: Cyrtologies of convergences, II: Sequential convergences, Math. Nachr. 127 (1986) 317–334.https://doi.org/10.1002/mana.19861270123Google Scholar
  6. S. Dolecki, G. H. Greco, A. Lechicki: Compactoid and compact filters, Pacific J. Math. 117 (1985) 69–98.https://doi.org/10.2140/pjm.1985.117.69Google Scholar
  7. S. Dolecki, J. Guillerme, M. B. Lignola, C. Malivert: Γ-inequalities and stability of generalized extremal convolutions, Math. Nachr. 152 (191) 299–323.https://doi.org/10.1002/mana.19911520123Google Scholar
  8. S. Dolecki, S. Kurcyusz: Convexité généralisée et optimisation, C. R. Acad. Sci., Paris, Sér. A 283 (1976) 91–94.Google Scholar
  9. S. Dolecki, S. Kurcyusz: On Φ-convexity in extremal problems, SIAM J. Control Optim. 16(2) (1978) 277–300.https://doi.org/10.1137/0316018Google Scholar
  10. S. Dolecki, M.-P. Moschen: Inequalities involving Γ-functionals and semi-complete lattice homomorphisms, Rend. Semin. Mat. Univ. Padova 137 (1984) 61–82.Google Scholar
  11. S. Dolecki, F. Mynard: Hyperconvergences, Appl. Gen. Topol. 4(2) (2003) 391–419.https://doi.org/10.4995/agt.2003.2041Google Scholar
  12. W. Fenchel: Convex Cones, Sets and Functions, Princeton University, Princeton (1953).Google Scholar
  13. E. De Giorgi, T. Franzoni: Su un tipo di convergenza variazionale, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 58 (1975) 842–850.Google Scholar
  14. G. H. Greco: Limitoidi e reticoli completi, Ann. Univ. Ferrara, N. Ser., Sez. VII 29 (1983) 153–164.https://doi.org/10.1007/BF02825049Google Scholar
  15. G. H. Greco: Decomposizioni di semifiltri e Γ-limiti sequenziali in reticoli completamente distributivi, Ann. Mat. Pura Appl., IV. Ser. 137 (1984) 61–82.https://doi.org/10.1007/BF01789389Google Scholar
  16. G. H. Greco: Limites et fonctions densemble, Rend. Sem. Mat. Univ. Padova 72 (1984) 89–97.Google Scholar
  17. J.-L. Joly: Une famille de topologies sur lensemble des fonctions convexes pour lesquelles la polarité est bicontinue, J. Math. Pures Appl., IX. Sér. 52 (1973) 421–441.Google Scholar
  18. J. J. Moreau: Fonctionnelles convexes, Séminaire Jean Leray 2 (1966–67) 1–108.Google Scholar
  19. J.-J. Moreau: Inf-convolutions, sous-additivité, convexité des fonctions numériques, J. Math. Pures Appl., IX. Sér. 49 (1970) 109–154.Google Scholar
  20. U. Mosco: On the continuity of Young-Fenchel transformations, J. Math. Anal. Appl. 35 (1971) 518–535.https://doi.org/10.1016/0022-247X(71)90200-9Google Scholar
  21. G. Peano: Formulaire Mathématique, 4th Ed., Bocca, Torino (1903).Google Scholar
  22. G. Peano: Formulario Mathematico, Bocca, Torino (1908).Google Scholar

Suggested citation

S. Dolecki. “Polarities and Generalized Extremal Convolutions.” Journal of Convex Analysis 23 (2016), No. 2, 603–614. https://doi.org/10.68381/jca23022

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2016. Rights now held by Banach Press LLC.