Extending holomorphic maps in infinite dimensions

Bui Dac Tac

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 3, page 241-253
  • ISSN: 0066-2216

Abstract

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Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in some special cases.

How to cite

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Bui Dac Tac. "Extending holomorphic maps in infinite dimensions." Annales Polonici Mathematici 54.3 (1991): 241-253. <http://eudml.org/doc/262261>.

@article{BuiDacTac1991,
abstract = {Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in some special cases.},
author = {Bui Dac Tac},
journal = {Annales Polonici Mathematici},
keywords = {Riemann domain modeled on a topological vector space; holomorphic mapping; holomorphic continuations to the envelope of holomorphy; L- space; finite dimensional extension property; Stein manifold; HZ-space; sequentially complete locally convex space; domain of existence of a Banach-valued holomorphic function},
language = {eng},
number = {3},
pages = {241-253},
title = {Extending holomorphic maps in infinite dimensions},
url = {http://eudml.org/doc/262261},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Bui Dac Tac
TI - Extending holomorphic maps in infinite dimensions
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 3
SP - 241
EP - 253
AB - Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in some special cases.
LA - eng
KW - Riemann domain modeled on a topological vector space; holomorphic mapping; holomorphic continuations to the envelope of holomorphy; L- space; finite dimensional extension property; Stein manifold; HZ-space; sequentially complete locally convex space; domain of existence of a Banach-valued holomorphic function
UR - http://eudml.org/doc/262261
ER -

References

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  12. [12] P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 89, 1984. 
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  17. [17] N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230. Zbl0333.32011

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