Obtaining the Fourier spectrum via Fourier coefficients
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913271864360960 |
|---|---|
| author | Carnovale, Marc Fraser, Jonathan M. de Orellana, Ana E. |
| author_facet | Carnovale, Marc Fraser, Jonathan M. de Orellana, Ana E. |
| contents | The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and are defined in terms of certain energies which capture Fourier decay. In this paper we obtain a convenient discrete representation of those energies using the Fourier coefficients. As an example application, we use this representation to establish sharp bounds for the Fourier spectrum of a general measure with bounded support, improving previous estimates of the second-named author |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Obtaining the Fourier spectrum via Fourier coefficients Carnovale, Marc Fraser, Jonathan M. de Orellana, Ana E. Classical Analysis and ODEs Functional Analysis primary: 28A75, 42B10, secondary: 42B05 The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and are defined in terms of certain energies which capture Fourier decay. In this paper we obtain a convenient discrete representation of those energies using the Fourier coefficients. As an example application, we use this representation to establish sharp bounds for the Fourier spectrum of a general measure with bounded support, improving previous estimates of the second-named author |
| title | Obtaining the Fourier spectrum via Fourier coefficients |
| topic | Classical Analysis and ODEs Functional Analysis primary: 28A75, 42B10, secondary: 42B05 |
| url | https://arxiv.org/abs/2403.12603 |