Publication: Spaces of holomorphic germs on quotients
Loading...
Full text at PDC
Publication Date
1993-01-01
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Let (X, Φ) be a Riemann domain over a complex Fréchet space E, K a compact subset of X and (K) the vector space of all holomorphic germs on K. Given an F-quotient (XF, φF, ψ) of (X, φ) (see the definition below), the canonical mapping ψ : X ↦ XF induces a mapping ψ* : g ∈ (ψ(K)) ↦ g ○ ψ ∈ (K). Our aim here is to study conditions under which ψ* is an embedding when natural topologies on spaces of germs are considered.
Description
UCM subjects
Unesco subjects
Keywords
Citation
J.M. Ansemil and S.Ponte. The compact open and the Nachbin ported topologies on spaces of holomorphic functions. Arch. Math. 51 (1988), 65-70.
J.M. Ansemil and Taskinen. On a problem of topologies in infinite dimensional holomorphy. Arch. Math. 54 (1990), 61-64.
R.M.Aron, L.A.Moraes and R.A.Ryan. Factorizaton of holomorphic mappings in infinite dimensions. Math. Ann. 277 (1987), 617-628.
S.F.Belenot. Basic sequences in non-Schwart—Fréchet spaces. Trans. Amer.Math. Soc. 258, n 1 (1980), 198-216
J.Bonet and J.C.Díaz. The problem of topologies of Groethendieck and the class of Fréchet T-space. Math.Nachr. 150(1991, 109-118.
S.Dineen.Complex analysis in locally convex spaces. North-Holland Math.Studies. vol.57,Noth-Holland, Amsterdam, 1981.
S.Dineen.Holomorphic functions on Frécet-Montel spaces. J.Math.Anal. Appl.163,n.2(1992), 581-587.
K.Floret. Fréchet-Montel spaces wich are not Schwart-spaces. Portugal.Math.42 (1983/1984), 1-4.
P.Galindo, D.García, and M.Maestre. The coincidence of τ0 and τw for spaces of holomorphic functions on some Frécet-Montel space. Proc.R.Ir.Acad. 91A, n.2 (1991), 137-143
J.Horvát. Topological vector spaces and distributions. Addison-Wesley, Reading, MA,1996.
L.A.Moraes, O.W.Paques, and C.Zaine. F-quotient and envelope of F-holomorphy, J.Math.Anal.Appl. 163,n.2(1992), 393-405.
J.Mujica. A Banach-Dieudonné theorem for germs of holomorphic functions. J.Funct.Anal.57, n.1(1984), 31-48.
S.Ponte. A remark about the embedding (H(E/F), τ) (H(E),τ) with τ=τ0,τw in Fréchet spaces. Note Math.9, n.2(1989), 217-220.