Spectral deviation of concentration operators for the short-time Fourier transform
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866917612020039680 |
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| author | Marceca, Felipe Romero, José Luis |
| author_facet | Marceca, Felipe Romero, José Luis |
| contents | Time-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. We estimate how much the corresponding eigenvalue counting function deviates from the Lebesgue measure of the time-frequency domain. For window functions in the Gelfand-Shilov class, the bounds almost match known asymptotics, with the advantage of being effective for concrete domains and spectral thresholds. As such our estimates allow for applications where the spectral threshold depends on the geometry of the time-frequency concentration domain. We also consider window functions that decay only polynomially in time and frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_06150 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Spectral deviation of concentration operators for the short-time Fourier transform Marceca, Felipe Romero, José Luis Spectral Theory Functional Analysis 47B35, 47G30, 42B35, 47A75, 42C40 Time-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. We estimate how much the corresponding eigenvalue counting function deviates from the Lebesgue measure of the time-frequency domain. For window functions in the Gelfand-Shilov class, the bounds almost match known asymptotics, with the advantage of being effective for concrete domains and spectral thresholds. As such our estimates allow for applications where the spectral threshold depends on the geometry of the time-frequency concentration domain. We also consider window functions that decay only polynomially in time and frequency. |
| title | Spectral deviation of concentration operators for the short-time Fourier transform |
| topic | Spectral Theory Functional Analysis 47B35, 47G30, 42B35, 47A75, 42C40 |
| url | https://arxiv.org/abs/2104.06150 |