On finite configurations in the spectra of singular measures
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913554566742016 |
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| author | Ayoush, Rami |
| author_facet | Ayoush, Rami |
| contents | We establish various forms of the following certainty principle: a set $S \subset \mathbb{R}^{n}$ contains a given finite linear pattern, provided that $S$ is a support of the Fourier transform of a sufficiently singular probability measure on $\mathbb{R}^{n}$. As its main corollary, we provide new dimensional estimates for PDE- and Fourier-constrained vector measures. Those results, in certain cases of restrictions given by homogeneous operators, improve known bounds related to the notion of the $k$-wave cone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12036 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On finite configurations in the spectra of singular measures Ayoush, Rami Classical Analysis and ODEs Analysis of PDEs We establish various forms of the following certainty principle: a set $S \subset \mathbb{R}^{n}$ contains a given finite linear pattern, provided that $S$ is a support of the Fourier transform of a sufficiently singular probability measure on $\mathbb{R}^{n}$. As its main corollary, we provide new dimensional estimates for PDE- and Fourier-constrained vector measures. Those results, in certain cases of restrictions given by homogeneous operators, improve known bounds related to the notion of the $k$-wave cone. |
| title | On finite configurations in the spectra of singular measures |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2108.12036 |