On multiple null-series in the Walsh system, M- and U- sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914213369217024 |
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| author | Kazakova, A. D. Plotnikov, M. G. |
| author_facet | Kazakova, A. D. Plotnikov, M. G. |
| contents | A family of M-sets and null-series for the d-dimensional Walsh system is constructed if we consider convergence over rectangles, cubes, or iterated convergence. Non-empty portions of the constructed M-sets are also M-sets. The question of the rate of convergence to zero of the coefficients of zero-series that realize the constructed M-sets is studied, and it is shown how to modify the construction of the latter to turn them into U-sets |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On multiple null-series in the Walsh system, M- and U- sets Kazakova, A. D. Plotnikov, M. G. Classical Analysis and ODEs A family of M-sets and null-series for the d-dimensional Walsh system is constructed if we consider convergence over rectangles, cubes, or iterated convergence. Non-empty portions of the constructed M-sets are also M-sets. The question of the rate of convergence to zero of the coefficients of zero-series that realize the constructed M-sets is studied, and it is shown how to modify the construction of the latter to turn them into U-sets |
| title | On multiple null-series in the Walsh system, M- and U- sets |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.00182 |