Polar Duality and the Donoho--Stark Uncertainty Principle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909607481311232 |
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| author | de Gosson, Maurice |
| author_facet | de Gosson, Maurice |
| contents | Polar duality is a fundamental geometric concept that can be interpreted as a form of Fourier transform between convex sets. Meanwhile, the Donoho-Stark uncertainty principle in harmonic analysis provides a framework for comparing the relative concentrations of a function and its Fourier transform. Combining the Blaschke--Santaló inequality from convex geometry with the Donoho--Stark principle, we establish estimates for the trade-off of concentration between a square integrable function in a symmetric convex body and that of its Fourier transform in the polar dual of that body. In passing, we use the Donoho-Stark uncertainty principle to establish a new concentration result for the Wigner function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_07037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polar Duality and the Donoho--Stark Uncertainty Principle de Gosson, Maurice Mathematical Physics 53-06 F.2.2 Polar duality is a fundamental geometric concept that can be interpreted as a form of Fourier transform between convex sets. Meanwhile, the Donoho-Stark uncertainty principle in harmonic analysis provides a framework for comparing the relative concentrations of a function and its Fourier transform. Combining the Blaschke--Santaló inequality from convex geometry with the Donoho--Stark principle, we establish estimates for the trade-off of concentration between a square integrable function in a symmetric convex body and that of its Fourier transform in the polar dual of that body. In passing, we use the Donoho-Stark uncertainty principle to establish a new concentration result for the Wigner function. |
| title | Polar Duality and the Donoho--Stark Uncertainty Principle |
| topic | Mathematical Physics 53-06 F.2.2 |
| url | https://arxiv.org/abs/2505.07037 |