Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915659502321664 |
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| author | Fan, Aihua Jiang, Kai Zhang, Pingwen |
| author_facet | Fan, Aihua Jiang, Kai Zhang, Pingwen |
| contents | For a class of $\mathbb{R}^d$-ations and $\mathbb{Z}^d$-actions on the $n$-dimensional torus $\mathbb{T}^n$, we characterize their unique ergodicity and establish a theorem of Weyl type. This result allows us to establish an isomorphism between the Banach algebra of quasi-periodic functions with spectrum in a given $\mathbb{Z}$-module and the Banach algebra of periodic functions on a torus. This, in return, allows us to give a very simple proof of Hausdorff-Young inequalities for Besicovitch almost periodic functions. The regularity of the parent function of a quasi-periodic function is also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions Fan, Aihua Jiang, Kai Zhang, Pingwen Classical Analysis and ODEs Dynamical Systems Number Theory Primary 42A75, 11K70, Scondary 43A25, 37A30 For a class of $\mathbb{R}^d$-ations and $\mathbb{Z}^d$-actions on the $n$-dimensional torus $\mathbb{T}^n$, we characterize their unique ergodicity and establish a theorem of Weyl type. This result allows us to establish an isomorphism between the Banach algebra of quasi-periodic functions with spectrum in a given $\mathbb{Z}$-module and the Banach algebra of periodic functions on a torus. This, in return, allows us to give a very simple proof of Hausdorff-Young inequalities for Besicovitch almost periodic functions. The regularity of the parent function of a quasi-periodic function is also studied. |
| title | Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions |
| topic | Classical Analysis and ODEs Dynamical Systems Number Theory Primary 42A75, 11K70, Scondary 43A25, 37A30 |
| url | https://arxiv.org/abs/2512.06821 |