Mixed-Fourier-norm spaces and holomorphic functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913626290388992 |
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| author | Avetisyan, Zhirayr Karapetyants, Alexey |
| author_facet | Avetisyan, Zhirayr Karapetyants, Alexey |
| contents | We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable functions, establishing their most basic properties. Then we consider the half-Fourier transform $f(x,y)\mapsto\hat f(ξ,y)$ in the first variable, and discuss the behaviour of function spaces on $G\times Y$ and $\hat G\times Y$ under this transform. We introduce general mixed-Fourier-norm spaces on $G\times Y$, and the subspaces of holomorphic functions among them, and give an explicit descriptions of the Fourier images of these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixed-Fourier-norm spaces and holomorphic functions Avetisyan, Zhirayr Karapetyants, Alexey Functional Analysis 30H20, 46E30, 46E15 We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable functions, establishing their most basic properties. Then we consider the half-Fourier transform $f(x,y)\mapsto\hat f(ξ,y)$ in the first variable, and discuss the behaviour of function spaces on $G\times Y$ and $\hat G\times Y$ under this transform. We introduce general mixed-Fourier-norm spaces on $G\times Y$, and the subspaces of holomorphic functions among them, and give an explicit descriptions of the Fourier images of these spaces. |
| title | Mixed-Fourier-norm spaces and holomorphic functions |
| topic | Functional Analysis 30H20, 46E30, 46E15 |
| url | https://arxiv.org/abs/2411.15379 |