Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2403.11712 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929353301950464 |
|---|---|
| author | Haak, Bernhard H. Haase, Markus |
| author_facet | Haak, Bernhard H. Haase, Markus |
| contents | Let $f = f(z,t)$ be a function holomorphic in $z \in O \subseteq {\mathbb C}^d$ for fixed $t\in Ω$ and measurable in $t$ for fixed $z$ and such that$z \mapsto f(z,\cdot)$ is bounded with values in$E := L_{p}(Ω)$, $1\le p \le \infty$. It is proved (among other things) that \[ \langle t\mapsto φ( f(\cdot,t) ) , μ\rangle= φ(z \mapsto \langle f(z, \cdot) , μ\rangle )\] whenever $μ\in E'$ and $φ$ is a linear functional on $H^\infty(O)$ that is sequentially continuous with respect to bounded pointwise convergence in $H^\infty(O)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vector-Valued Holomorphic Functions and Abstract Fubini-Type Theorems Haak, Bernhard H. Haase, Markus Functional Analysis Let $f = f(z,t)$ be a function holomorphic in $z \in O \subseteq {\mathbb C}^d$ for fixed $t\in Ω$ and measurable in $t$ for fixed $z$ and such that$z \mapsto f(z,\cdot)$ is bounded with values in$E := L_{p}(Ω)$, $1\le p \le \infty$. It is proved (among other things) that \[ \langle t\mapsto φ( f(\cdot,t) ) , μ\rangle= φ(z \mapsto \langle f(z, \cdot) , μ\rangle )\] whenever $μ\in E'$ and $φ$ is a linear functional on $H^\infty(O)$ that is sequentially continuous with respect to bounded pointwise convergence in $H^\infty(O)$. |
| title | Vector-Valued Holomorphic Functions and Abstract Fubini-Type Theorems |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2403.11712 |