Complutense University Library

Spaces of holomorphic germs on quotients

Ansemil, José María M. and Ponte, Socorro (1993) Spaces of holomorphic germs on quotients. Journal of Mathematical Analysis and Applications, 172 (1). pp. 33-38. ISSN 0022-247X

[img] PDF
Restricted to Repository staff only until 31 December 2020.


Official URL:

View download statistics for this eprint

==>>> Export to other formats


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.

Item Type:Article
Uncontrolled Keywords:Riemann domain over a complex Fréchet space; space of all holomorphic germs
Subjects:Sciences > Mathematics > Functions
ID Code:16811

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.

Deposited On:23 Oct 2012 08:24
Last Modified:07 Feb 2014 09:36

Repository Staff Only: item control page