On UC-multipliers for multiple trigonometric systems
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911656200634368 |
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| author | Karagulyan, Grigori A. |
| author_facet | Karagulyan, Grigori A. |
| contents | We investigate the class of sequences $w(n)$ that can serve as almost-everywhere convergence Weyl multipliers for all rearrangements of multiple trigonometric systems. We show that any such sequence must satisfy the bounds $\log n\lesssim w(n)\lesssim\log^2 n$. Our main result establishes a general equivalence principle between one-dimensional and multidimensional trigonometric systems, which allows one to extend certain estimates known for the one-dimensional case to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10360 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On UC-multipliers for multiple trigonometric systems Karagulyan, Grigori A. Classical Analysis and ODEs 42C05, 42C10, 28D05 We investigate the class of sequences $w(n)$ that can serve as almost-everywhere convergence Weyl multipliers for all rearrangements of multiple trigonometric systems. We show that any such sequence must satisfy the bounds $\log n\lesssim w(n)\lesssim\log^2 n$. Our main result establishes a general equivalence principle between one-dimensional and multidimensional trigonometric systems, which allows one to extend certain estimates known for the one-dimensional case to higher dimensions. |
| title | On UC-multipliers for multiple trigonometric systems |
| topic | Classical Analysis and ODEs 42C05, 42C10, 28D05 |
| url | https://arxiv.org/abs/2601.10360 |