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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.18769 |
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| _version_ | 1866914334412636160 |
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| author | Svela, Erling A. T. |
| author_facet | Svela, Erling A. T. |
| contents | Daubechies-type theorems for localization operators are established in the multi-variate setting, where Hagedorn wavepackets are identified as the proper substitute of the Hermite functions. The class of Reinhardt domains is shown to be the natural class of masks that allow for a Daubechies-type result. Daubechies' classical theorem is a consequence of double orthogonality results for the short-time Fourier transform. We extend double orthogonality to the quantum setting and use it to establish Daubechies-type theorems for mixed-state localization operators, a key notion of quantum harmonic analysis. Lastly, we connect the results to Toeplitz operators on quantum Gabor spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extensions of Daubechies' theorem: Reinhardt domains, Hagedorn wavepackets and mixed-state localization operators Svela, Erling A. T. Functional Analysis Complex Variables 42C40, 47G30 (Primary) 47B35, 42C05, 32Q02 (Secondary) Daubechies-type theorems for localization operators are established in the multi-variate setting, where Hagedorn wavepackets are identified as the proper substitute of the Hermite functions. The class of Reinhardt domains is shown to be the natural class of masks that allow for a Daubechies-type result. Daubechies' classical theorem is a consequence of double orthogonality results for the short-time Fourier transform. We extend double orthogonality to the quantum setting and use it to establish Daubechies-type theorems for mixed-state localization operators, a key notion of quantum harmonic analysis. Lastly, we connect the results to Toeplitz operators on quantum Gabor spaces. |
| title | Extensions of Daubechies' theorem: Reinhardt domains, Hagedorn wavepackets and mixed-state localization operators |
| topic | Functional Analysis Complex Variables 42C40, 47G30 (Primary) 47B35, 42C05, 32Q02 (Secondary) |
| url | https://arxiv.org/abs/2410.18769 |