Vector-Valued Holomorphic Functions and Abstract Fubini-Type Theorems
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HAAK, Bernhard H. | |
| hal.structure.identifier | Mathematisches Seminar [Kiel] | |
| dc.contributor.author | HAASE, Markus | |
| dc.date.accessioned | 2024-04-04T02:29:43Z | |
| dc.date.available | 2024-04-04T02:29:43Z | |
| dc.date.created | 2024-03-16 | |
| dc.date.issued | 2024-03-16 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190203 | |
| dc.description.abstractEn | Let $f = f(z,t)$ be a function holomorphic in $z \in O \subseteq {\mathbb C}^d$ for fixed $t\in \Omega$ and measurable in $t$ for fixed $z$ and such that$z \mapsto f(z,\cdot)$ is bounded with values in$E := L_{p}(\Om)$, $1\le p \le \infty$. It is proved (among other things) that \[ \langle t\mapsto \varphi( f(\cdot,t) ) , \mu \rangle= \varphi(z \mapsto \langle f(z, \cdot) , \mu\rangle )\] whenever $\mu \in E'$ and $\varphi$ is a linear functional on $H^\infty(O)$ that is sequentially continuous with respect to bounded pointwise convergence in $H^\infty(O)$. | |
| dc.language.iso | en | |
| dc.rights.uri | http://hal.archives-ouvertes.fr/licences/copyright/ | |
| dc.subject.en | vector-valued | |
| dc.subject.en | holomorphic functions of several variables | |
| dc.title.en | Vector-Valued Holomorphic Functions and Abstract Fubini-Type Theorems | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04507545 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04507545v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2024-03-16&rft.au=HAAK,%20Bernhard%20H.&HAASE,%20Markus&rft.genre=preprint |
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