The Work of the Mathematician Leopoldo Nachbin (1922-1993) from FNFi
DOI:
10.47976/RBHM2019v19n38183-103Palavras-chave:
Leopoldo Nachbin, Mathematical Analysis, FNFi, Brazilian mathematical communityResumo
In this paper we discuss the professional activity of Leopoldo Nachbin (1922-1993) in the period in which he worked at National Faculty of Philosophy of the University of Brazil (FNFi/UB, in Portuguese) until his retirement by Institute of Mathematics of the Federal University of Rio de Janeiro (IM/UFRJ, in Portuguese). We identify the influence played by some mathematicians such as G. Mammana (1893-1980), L. Schwartz (1915-2002), A. Monteiro (1907-1980), A. Weil (1906-1998), J. Dieudonné (1906-1992), M. Stone (1903-1989), and A. A. Albert (1905-1972) in the professional training of L. Nachbin. We also address the serious difficulties he encountered in the Mathematics Department of FNFi when he was entered in the competition, opened in 1950, for the post of full Professor (Professor Catedrático) of Mathematics and Superior Analysis of FNFi. We emphasize in the paper, that the period from 1947 to the 1960s marks the most creative and productive phase in terms of scientific research in the academic life of L. Nachbin.
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BARANY, M. J.; PAUMIER, A-S.; LÜTZEN, J. From Nancy to Copenhagen to the World: The internationalization of Laurent Schwartz and his theory of distributions. Hist. Math. vol. 44, nº 4, p. 367-394, 2017.
BARROSO, J. A.; MATOS, M. C.; NACHBIN, L. On holomorphy versus linearity in classifying locally convex spaces. Infin. Dim. Holom. Appl. Proc. Int. Symp. UNICAMP, 1975, p. 31-74, 1977. (Zbl 0399.46034).
BOURBAKI, N. Topologie Generale. Paris: Herman & Cia. Éditeurs, 1951. Chapitre II.
DAY, M. M. Normed linear spaces. Berlin: Springer-Verlag, 1973.
DIAS, C. L. da S.; HÖNIG, C. S.; MEDEIROS, L. A. da J. Leopoldo Nachbin. Comp. Appl. Math., vol. 13, nº 3, p. 173-174, 1994.
DIEUDONNÉ, J. Análise Harmônica. Publicação nº 9, Rio de Janeiro: FNFi, 1952. Notas de aulas redigidas por J. Abdelhay.
______. Recent developments in the theory of locally convex vector spaces. Bull. Amer. Math. Soc., vol. 59, p. 495-512, 1953.
FUCHSSTEINER, B.; LUSKY, W. Convex Cones. North – Holland Math. Stud. 56 – Notas Mat. 82, Amsterdam, 1981.
GOMES, R. L. Homenagem a Leopoldo Nachbin. Gazeta de Matemática. Anos 34-35, nºs. 129-132, p. 7-11, 1973-1974.
GOODNER, D. B. Projections in normed linear spaces. Trans. Amer. Math. Soc., vol. 69, nº 1, p. 89-108, 1950.
GROTHENDIECK, A.; DIEUDONNÉ, J. Eléments de géométrie algébrique I, Grundlehren Math. Wiss., 166, p. 236-246, 1971.
HÖNIG, C. S. Teoria das distribuições. São Paulo: IME/USP, s.d.
HORVÁTH, J. The life and Works of Leopoldo Nachbin, in BARROSO, J. A.(editor). Aspects of Mathematics and its applications. Elsevier Science Publishers B. V., 1986.
______. The late works of Leopoldo Nachbin. Com. Appl. Math. vol. 13, nº 3, p. 175 -188, 1994.
IBBD/CNPq. Notícias. Noticiário do IMPA. Rio de Janeiro: 1969.
LOTZ, H. P. Extension and liftings of positive linear mapping on Banach Lattices. Trans. Amer. Math. Soc., vol. 211, p. 85-100, 1975.
LÜTZEN, J. The Prehistory of the Theory of Distributions. Berlin: Springer-Verlag, 1982.
MACHADO, S. (Ed.). Functional Analysis, Holomorphy, and Approximation Theory. Lectures Notes Math. Berlin: Springer, 1981.
MAST. Arquivo Leopoldo Nachbin. Inventário Sumário. Rio de Janeiro: MAST, 1997.
MATOS, M. C. (Ed.). Infinite Dimensional Holomorphy and Applications. North-Holland Math. Stud. 12, Amsterdam, 1977.
MATOS, M. C.; NACHBIN, L. Reinhart domains of holomorphy in Banach spaces. Adv. Math. vol. 92, p. 266-278, 1992. (MR 93d:46069).
MEDEIROS, L. A.; MIRANDA, M. MILLA. Espaços de Sobolev (Iniciação aos Problemas Elíticos não Homogêneos). Rio de Janeiro: IM/UFRJ, 2000.
NACHBIN, L. Sobre a permutabilidade entre operações de passagem ao limite e de integração de equações diferenciais. An. Acad. Bras. Ciênc., tomo 13, p. 327-335, 1941.
______. Un estensione di un lemma di Dirichlet. Atti. Accad. Italia Rend., vol. 3, p. 204-208, 1942.
______. Une propriété charactéristique des algèbres booleiènnes. Port. Math. vol. 6, p. 115 – 118, 1947.
______. Combinação de topologias pseudo - metrisáveis e metrisáveis. Notas de Matemática nº 1, Rio de Janeiro: Universidade do Brasil, 1947.
______. Sur les espaces topologiques ordonnés, C. R. Acad. Sci. Paris, vol. 226, p. 381-382, 1948a. (MR, 9, 367).
______. Sur les espaces uniformisables ordonnés. C. R. Acad. Sci. Paris, vol. 226, p. 547, 1948b. (MR 9, 367).
______. Sur les espaces uniformes ordonnés. C. R. Acad. Sci. Paris, vol. 226, p. 774-775, 1948c. (MR 9, 455).
______. Sur les algèbres denses de fonctions différentiables sur une variété. C. R. Acad. Sci. Paris, vol. 228, p. 1549-1551, 1949.
______. On the Hahn-Banach Theorem. An. Acad. Bras. Ciênc., tomo 21, nº 2, p. 151-154, 1949b. (MR 11, 114).
______. On strictly minimal topological division rings. Bull. Amer. Math. Soc. vol. 55, nº 12, p. 1128-1136, 1949c.
______. A theorem of the Hahn-Banach type for linear transformations. Trans. Amer. Math. Soc.,v. 68, p. 28-46, 1950. (MR 11, 369), (MR 32932 46.3X), (MathSciNet 0032932), (Zbl 0035.35402, v. 35, p.354).
______. Topologia e ordem. Univ. Chicago Press, 1950a. Tese apresentada ao concurso para o cargo de professor Catedrático de Análise Matemática e Superior, FNFi/UB em 1950. (Zbl 0333. 54002).
______. Some problems in extending and lifting continuous linear transformations. Proceedings of the International Symposium on Linear Spaces. Hebrew University of Jerusalem, 1950b.
______. On a duality theorem for commutative groups. An. Acad. Bras. Ciênc., tomo 24, p. 137-142, 1952. (MR 16, 156).
______. Topological vector spaces of continuous functions. Proc. Nat. Acad. Sci, vol. 40, nº 6, p. 471- 474, 1954.
______. Résultats récents et problèmes de nature algébrique em théorie de l’approximation. Stockholm: Proc. Internat. Congress Math., 1962. (MR 31, 548).
______. Sur l’Abondance des Points Extrémaux d’un Ensemble Convexe Borné et Fermé. An. Acad. Bras. Ciênc., vol. 34, p. 445-448, 1962b. (MR 26, 6736).
______. Elements of approximation theory. Rochester: University of Rochester, 1964. Reimpresso em Van Nostrand Mathematical Studies, 14, 1967, D. Van Nostrand Company, New York.
______. Sur les espaces vectoriels topologiques d’applications continues. C. R. Acad. Sci. Paris, vol. 271, p. 596-598, 1970. (MR 42, 6593).
______.(Ed.). Functional Analysis and Applications. Lectures Notes in Math, vol. 384. Berlin: 1974.
______.(Ed.). Analise Fonctionelle et Applictions. Ed. Hermann: Paris, 1975.
______. The influence of António A. Ribeiro Monteiro in the development of Mathematics in Brazil. Port. Math., vol. 39, fasc. 1- 4, 1980.
_____¬_. A glance at holomorphic factorization and uniform holomorphy, Complex Analysis, Functional Analysis and Approximation Theory. North – Holland Math. Stud. 125. Notas Mat. 110, North- Holland, Amsterdam, p. 221-245, 1986, (MR 88h: 46085).
______. A profile of probability. Campinas: EdUNICAMP, 1987.
______. On the weighted approximation of continuously differentiable functions. Proc. Amer. Math. Soc., vol. 111, p. 481—485, 1991. (MR 91f: 41028).
______. Compact unions of closed subsets are closed and compact intersections of open subsets are open. Port. Math., vol. 49, nº 4, p. 403-409, 1992.
______. Convex cones and convex sets. Port. Math., vol. 50, nº 4, p. 467-487, 1993. (Zbl 0808.46015).
______. When does finite holomorphy imply holomorphy? Port. Math. vol. 51, nº 4, p.525-528, 1994. (Zbl 0870. 46030).
______. Convex sets, convex cones, affine spaces and affine cones. Rev. Colomb. Mat. vol. 30, nº 1, p. 1-23, 1996. (Zbl 0891.52001).
SCHWARTZ, L. Radon measures on arbitrary topological spaces and cylindrical measures. Tata Institute for Fundamental Research. Studies in Mathematics 6. Oxford University Press, 1973.
SILVA, C. P. da. Início e Consolidação da Pesquisa em Matemática no Brasil. 2ª Ed., Rio de Janeiro: Editora Ciência Moderna, 2013.
SILVA DIAS, C. L. da; HÖNIG, C. S.; MEDEIROS, L. A. da J. Leopoldo Nachbin. Comp. Appl. Math., vol, 13, nº 3, p. 173 -174, 1994.
SHIROTA, T. On locally convex vector spaces of continuous functions. Proc. Japan Acad., vol. 30, p. 294-298, 1954.
STONE, M. H. Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc., vol.41, p. 375 – 481, 1937.
PROLLA, J. B. Intersections of balls and approximation of vector valued functions. Aproximation Theory V, 1986. Aproximation Theory V. New York: Academic Press, p. 523-525, 1986.
______. A generalized Bernstein approximation theorem. Mathematical Proceedings of the Cambridge Philosophical Society , v. 104, p. 317-330, 1988.
WEIL, A. Sur les Espaces à Structure Uniforme et sur la Topologie Générale. Paris: Herman & Cia., Éditeurs, 1937.
ZAPATA, G. I. Bernstein approximation problem for differentiable functions and quasi-analytic weighted. Trans. Amer. Math. Soc., vol. 182, p. 503-509, 1973.
BARROSO, J. A.; MATOS, M. C.; NACHBIN, L. On holomorphy versus linearity in classifying locally convex spaces. Infin. Dim. Holom. Appl. Proc. Int. Symp. UNICAMP, 1975, p. 31-74, 1977. (Zbl 0399.46034).
BOURBAKI, N. Topologie Generale. Paris: Herman & Cia. Éditeurs, 1951. Chapitre II.
DAY, M. M. Normed linear spaces. Berlin: Springer-Verlag, 1973.
DIAS, C. L. da S.; HÖNIG, C. S.; MEDEIROS, L. A. da J. Leopoldo Nachbin. Comp. Appl. Math., vol. 13, nº 3, p. 173-174, 1994.
DIEUDONNÉ, J. Análise Harmônica. Publicação nº 9, Rio de Janeiro: FNFi, 1952. Notas de aulas redigidas por J. Abdelhay.
______. Recent developments in the theory of locally convex vector spaces. Bull. Amer. Math. Soc., vol. 59, p. 495-512, 1953.
FUCHSSTEINER, B.; LUSKY, W. Convex Cones. North – Holland Math. Stud. 56 – Notas Mat. 82, Amsterdam, 1981.
GOMES, R. L. Homenagem a Leopoldo Nachbin. Gazeta de Matemática. Anos 34-35, nºs. 129-132, p. 7-11, 1973-1974.
GOODNER, D. B. Projections in normed linear spaces. Trans. Amer. Math. Soc., vol. 69, nº 1, p. 89-108, 1950.
GROTHENDIECK, A.; DIEUDONNÉ, J. Eléments de géométrie algébrique I, Grundlehren Math. Wiss., 166, p. 236-246, 1971.
HÖNIG, C. S. Teoria das distribuições. São Paulo: IME/USP, s.d.
HORVÁTH, J. The life and Works of Leopoldo Nachbin, in BARROSO, J. A.(editor). Aspects of Mathematics and its applications. Elsevier Science Publishers B. V., 1986.
______. The late works of Leopoldo Nachbin. Com. Appl. Math. vol. 13, nº 3, p. 175 -188, 1994.
IBBD/CNPq. Notícias. Noticiário do IMPA. Rio de Janeiro: 1969.
LOTZ, H. P. Extension and liftings of positive linear mapping on Banach Lattices. Trans. Amer. Math. Soc., vol. 211, p. 85-100, 1975.
LÜTZEN, J. The Prehistory of the Theory of Distributions. Berlin: Springer-Verlag, 1982.
MACHADO, S. (Ed.). Functional Analysis, Holomorphy, and Approximation Theory. Lectures Notes Math. Berlin: Springer, 1981.
MAST. Arquivo Leopoldo Nachbin. Inventário Sumário. Rio de Janeiro: MAST, 1997.
MATOS, M. C. (Ed.). Infinite Dimensional Holomorphy and Applications. North-Holland Math. Stud. 12, Amsterdam, 1977.
MATOS, M. C.; NACHBIN, L. Reinhart domains of holomorphy in Banach spaces. Adv. Math. vol. 92, p. 266-278, 1992. (MR 93d:46069).
MEDEIROS, L. A.; MIRANDA, M. MILLA. Espaços de Sobolev (Iniciação aos Problemas Elíticos não Homogêneos). Rio de Janeiro: IM/UFRJ, 2000.
NACHBIN, L. Sobre a permutabilidade entre operações de passagem ao limite e de integração de equações diferenciais. An. Acad. Bras. Ciênc., tomo 13, p. 327-335, 1941.
______. Un estensione di un lemma di Dirichlet. Atti. Accad. Italia Rend., vol. 3, p. 204-208, 1942.
______. Une propriété charactéristique des algèbres booleiènnes. Port. Math. vol. 6, p. 115 – 118, 1947.
______. Combinação de topologias pseudo - metrisáveis e metrisáveis. Notas de Matemática nº 1, Rio de Janeiro: Universidade do Brasil, 1947.
______. Sur les espaces topologiques ordonnés, C. R. Acad. Sci. Paris, vol. 226, p. 381-382, 1948a. (MR, 9, 367).
______. Sur les espaces uniformisables ordonnés. C. R. Acad. Sci. Paris, vol. 226, p. 547, 1948b. (MR 9, 367).
______. Sur les espaces uniformes ordonnés. C. R. Acad. Sci. Paris, vol. 226, p. 774-775, 1948c. (MR 9, 455).
______. Sur les algèbres denses de fonctions différentiables sur une variété. C. R. Acad. Sci. Paris, vol. 228, p. 1549-1551, 1949.
______. On the Hahn-Banach Theorem. An. Acad. Bras. Ciênc., tomo 21, nº 2, p. 151-154, 1949b. (MR 11, 114).
______. On strictly minimal topological division rings. Bull. Amer. Math. Soc. vol. 55, nº 12, p. 1128-1136, 1949c.
______. A theorem of the Hahn-Banach type for linear transformations. Trans. Amer. Math. Soc.,v. 68, p. 28-46, 1950. (MR 11, 369), (MR 32932 46.3X), (MathSciNet 0032932), (Zbl 0035.35402, v. 35, p.354).
______. Topologia e ordem. Univ. Chicago Press, 1950a. Tese apresentada ao concurso para o cargo de professor Catedrático de Análise Matemática e Superior, FNFi/UB em 1950. (Zbl 0333. 54002).
______. Some problems in extending and lifting continuous linear transformations. Proceedings of the International Symposium on Linear Spaces. Hebrew University of Jerusalem, 1950b.
______. On a duality theorem for commutative groups. An. Acad. Bras. Ciênc., tomo 24, p. 137-142, 1952. (MR 16, 156).
______. Topological vector spaces of continuous functions. Proc. Nat. Acad. Sci, vol. 40, nº 6, p. 471- 474, 1954.
______. Résultats récents et problèmes de nature algébrique em théorie de l’approximation. Stockholm: Proc. Internat. Congress Math., 1962. (MR 31, 548).
______. Sur l’Abondance des Points Extrémaux d’un Ensemble Convexe Borné et Fermé. An. Acad. Bras. Ciênc., vol. 34, p. 445-448, 1962b. (MR 26, 6736).
______. Elements of approximation theory. Rochester: University of Rochester, 1964. Reimpresso em Van Nostrand Mathematical Studies, 14, 1967, D. Van Nostrand Company, New York.
______. Sur les espaces vectoriels topologiques d’applications continues. C. R. Acad. Sci. Paris, vol. 271, p. 596-598, 1970. (MR 42, 6593).
______.(Ed.). Functional Analysis and Applications. Lectures Notes in Math, vol. 384. Berlin: 1974.
______.(Ed.). Analise Fonctionelle et Applictions. Ed. Hermann: Paris, 1975.
______. The influence of António A. Ribeiro Monteiro in the development of Mathematics in Brazil. Port. Math., vol. 39, fasc. 1- 4, 1980.
_____¬_. A glance at holomorphic factorization and uniform holomorphy, Complex Analysis, Functional Analysis and Approximation Theory. North – Holland Math. Stud. 125. Notas Mat. 110, North- Holland, Amsterdam, p. 221-245, 1986, (MR 88h: 46085).
______. A profile of probability. Campinas: EdUNICAMP, 1987.
______. On the weighted approximation of continuously differentiable functions. Proc. Amer. Math. Soc., vol. 111, p. 481—485, 1991. (MR 91f: 41028).
______. Compact unions of closed subsets are closed and compact intersections of open subsets are open. Port. Math., vol. 49, nº 4, p. 403-409, 1992.
______. Convex cones and convex sets. Port. Math., vol. 50, nº 4, p. 467-487, 1993. (Zbl 0808.46015).
______. When does finite holomorphy imply holomorphy? Port. Math. vol. 51, nº 4, p.525-528, 1994. (Zbl 0870. 46030).
______. Convex sets, convex cones, affine spaces and affine cones. Rev. Colomb. Mat. vol. 30, nº 1, p. 1-23, 1996. (Zbl 0891.52001).
SCHWARTZ, L. Radon measures on arbitrary topological spaces and cylindrical measures. Tata Institute for Fundamental Research. Studies in Mathematics 6. Oxford University Press, 1973.
SILVA, C. P. da. Início e Consolidação da Pesquisa em Matemática no Brasil. 2ª Ed., Rio de Janeiro: Editora Ciência Moderna, 2013.
SILVA DIAS, C. L. da; HÖNIG, C. S.; MEDEIROS, L. A. da J. Leopoldo Nachbin. Comp. Appl. Math., vol, 13, nº 3, p. 173 -174, 1994.
SHIROTA, T. On locally convex vector spaces of continuous functions. Proc. Japan Acad., vol. 30, p. 294-298, 1954.
STONE, M. H. Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc., vol.41, p. 375 – 481, 1937.
PROLLA, J. B. Intersections of balls and approximation of vector valued functions. Aproximation Theory V, 1986. Aproximation Theory V. New York: Academic Press, p. 523-525, 1986.
______. A generalized Bernstein approximation theorem. Mathematical Proceedings of the Cambridge Philosophical Society , v. 104, p. 317-330, 1988.
WEIL, A. Sur les Espaces à Structure Uniforme et sur la Topologie Générale. Paris: Herman & Cia., Éditeurs, 1937.
ZAPATA, G. I. Bernstein approximation problem for differentiable functions and quasi-analytic weighted. Trans. Amer. Math. Soc., vol. 182, p. 503-509, 1973.
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SILVA, Clovis Pereira da. The Work of the Mathematician Leopoldo Nachbin (1922-1993) from FNFi. Revista Brasileira de História da Matemática, São Paulo, v. 19, n. 38, p. 183–103, 2020. DOI: 10.47976/RBHM2019v19n38183-103. Disponível em: https://www.rbhm.org.br/index.php/RBHM/article/view/9. Acesso em: 31 out. 2024.
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