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July 2009 Holomorphic functions taking values in a quotient of Fréchet-Schwartz spaces
Belmesnaoui Aqzzouz, Hassan M. El Alj
Hiroshima Math. J. 39(2): 277-292 (July 2009). DOI: 10.32917/hmj/1249046340

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.

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Belmesnaoui Aqzzouz. Hassan M. El Alj. "Holomorphic functions taking values in a quotient of Fréchet-Schwartz spaces." Hiroshima Math. J. 39 (2) 277 - 292, July 2009. https://doi.org/10.32917/hmj/1249046340

Information

Published: July 2009
First available in Project Euclid: 31 July 2009

zbMATH: 1191.46033
MathSciNet: MR2543653
Digital Object Identifier: 10.32917/hmj/1249046340

Subjects:
Primary: 46M05, 46MXX, 46T25

Rights: Copyright © 2009 Hiroshima University, Mathematics Program

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Vol.39 • No. 2 • July 2009
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