Factorization of uniformly holomorphic functions

• Autorzy: Luiza A. Moraes , Otilia W. Paques , M. Carmelina F. Zaine
• Języki publikacji: EN

Abstrakty

EN

Let E be a complex Hausdorff locally convex space such that the strong dual E' of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the pull-back $ε*_{u}(U)$ of the envelope of uniform holomorphy of Π(U) constructed by Paques and Zaine [9] is the envelope of uF-holomorphy of U.

Słowa kluczowe

EN

uniformly holomorphic; envelope of holomorphy

Kategorie tematyczne

• 46G20: Infinite-dimensional holomorphy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 61
• Numer: 1
• Strony: 1-11

Daty

wydano

1995

otrzymano

1992-04-13

poprawiono

1994-04-11

Twórcy

autor

Luiza A. Moraes

• Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, CEP 21945-970 Rio de Janeiro, RJ, Brasil

autor

Otilia W. Paques

• Departamento de Matemática, Instituto de Matemática, Estatística e Ciência da Computação, Universidade Estadual de Campinas, C.P. 6065, CEP 13081-970 Campinas, SP, Brasil

autor

M. Carmelina F. Zaine

• Departamento de Matemática, Instituto de Matemática, Estatística e Ciência da Computação, Universidade Estadual de Campinas, C.P. 6065, CEP 13081-970 Campinas, SP, Brasil

Bibliografia

• [1] R. Aron, L. Moraes and R. Ryan, Factorization of holomorphic mappings in infinite dimensions, Math. Ann. 277 (1987), 617-628.
• [2] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, Amsterdam, 1981.
• [3] P. Hilton, Tópicos de Álgebra Homológica, 8º Colóquio Brasileiro de Matemática, IME-Universidade de S ao Paulo, Brasil, 1971.
• [4] L. Moraes, O. W. Paques and M. C. F. Zaine, F-quotients and envelope of F-holomorphy, J. Math. Anal. Appl. 163 (2) (1992), 393-405.
• [5] J. Mujica, Domain of holomorphy in (DFC)-spaces, in: Functional Analysis, Holomorphy and Approximation Theory, Lecture Notes in Math. 843, Springer, Berlin, 1980, 500-533.
• [6] L. Nachbin, Uniformité d'holomorphie et type exponentiel, in: Séminaire P. Lelong 1970, Lectures Notes in Math. 205, Springer, Berlin, 1971, 216-224.
• [7] L. Nachbin, Recent developments in infinite dimensional holomorphy, Bull. Amer. Math. Soc. 79 (1973), 625-640.
• [8] L. Nachbin, On pure uniform holomorphy in spaces of holomorphic germs, Results in Math. 8 (1985), 117-122.
• [9] O. W. Paques and M. C. Zaine, Uniformly holomorphic continuation, J. Math. Anal. Appl. 123 (2) (1987), 448-454.
• [10] M. Schottenloher, The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition, Ann. Inst. Fourier (Grenoble) 26 (4) (1976), 207-237.