Fourier transform of BV functions and applications
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913595115175936 |
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| author | Beretti, Thomas Gennaioli, Luca |
| author_facet | Beretti, Thomas Gennaioli, Luca |
| contents | This paper investigates the relation between the Fourier transform of {\rm BV} (bounded variation) functions and their jump sets. We introduce the notion of $L^2$-jump product and obtain a weighted Plancherel identity for {\rm BV} functions. As a corollary, we get a newfound characterization of sets of finite perimeter in terms of their Fourier transform. Moreover, we sharpen a result of Herz on the set-theoretic derivative of the Fourier transform of characteristic functions of sets. Last, we obtain sharp bounds on the quadratic discrepancy of {\rm BV} functions, and as a consequence, we generalize the classic estimates of Beck and Montgomery. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier transform of BV functions and applications Beretti, Thomas Gennaioli, Luca Classical Analysis and ODEs Functional Analysis Number Theory This paper investigates the relation between the Fourier transform of {\rm BV} (bounded variation) functions and their jump sets. We introduce the notion of $L^2$-jump product and obtain a weighted Plancherel identity for {\rm BV} functions. As a corollary, we get a newfound characterization of sets of finite perimeter in terms of their Fourier transform. Moreover, we sharpen a result of Herz on the set-theoretic derivative of the Fourier transform of characteristic functions of sets. Last, we obtain sharp bounds on the quadratic discrepancy of {\rm BV} functions, and as a consequence, we generalize the classic estimates of Beck and Montgomery. |
| title | Fourier transform of BV functions and applications |
| topic | Classical Analysis and ODEs Functional Analysis Number Theory |
| url | https://arxiv.org/abs/2407.13347 |