Generic measures with slowly decaying Fourier coefficients
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911361676607488 |
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| author | Limani, Adem |
| author_facet | Limani, Adem |
| contents | We investigate threshold phenomena in weighted $\ell^2$-spaces and characterize the critical regimes where elements with either small support or maximally bad range can be constructed. Our results are shown to be optimal in several respects, and our proofs principally rely on techniques involving sparse Fourier spectrum. We further show that these seemingly pathological constructions are actually generic from certain categorical perspectives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic measures with slowly decaying Fourier coefficients Limani, Adem Functional Analysis Classical Analysis and ODEs 42A16, 42A55 We investigate threshold phenomena in weighted $\ell^2$-spaces and characterize the critical regimes where elements with either small support or maximally bad range can be constructed. Our results are shown to be optimal in several respects, and our proofs principally rely on techniques involving sparse Fourier spectrum. We further show that these seemingly pathological constructions are actually generic from certain categorical perspectives. |
| title | Generic measures with slowly decaying Fourier coefficients |
| topic | Functional Analysis Classical Analysis and ODEs 42A16, 42A55 |
| url | https://arxiv.org/abs/2508.02361 |