## Hiroshima Mathematical Journal

### Holomorphic functions taking values in a quotient of Fréchet-Schwartz spaces

#### Abstract

We define a space of holomorphic functions $O_{1}(U,E\mid F)$ on a domain of holomorphy $U$ of ${\Bbb C}^{n}$, taking their values in quotient bornological spaces $E\mid F$ as the kernel of a sheaf-morphism. We show that if $E$ is a Schwartz $b$-space and $F$ is a Fréchet-Schwartz $b$-space, then $O_{1}(U,E\mid F)$ and $O\left( U,E\right) \mid O\left( U,F\right)$ are naturally isomorphic.

#### Article information

Source
Hiroshima Math. J., Volume 39, Number 2 (2009), 277-292.

Dates
First available in Project Euclid: 31 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1249046340

Digital Object Identifier
doi:10.32917/hmj/1249046340

Mathematical Reviews number (MathSciNet)
MR2543653

Zentralblatt MATH identifier
1191.46033

#### Citation

Aqzzouz, Belmesnaoui; El Alj, Hassan M. Holomorphic functions taking values in a quotient of Fréchet-Schwartz spaces. Hiroshima Math. J. 39 (2009), no. 2, 277--292. doi:10.32917/hmj/1249046340. https://projecteuclid.org/euclid.hmj/1249046340