Heisenberg-smooth operators from the phase space perspective
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908477342875648 |
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| author | Fulsche, Robert van Luijk, Lauritz |
| author_facet | Fulsche, Robert van Luijk, Lauritz |
| contents | Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) We can admit general quantization schemes, (2) allow for other phase space geometries, (3) obtain Schatten class analogs of the result, and (4) are able to characterize precisely 'Heisenberg-analytic' operators. For (3), we use QHA to derive Schatten versions of the Calderón-Vaillancourt theorem, which might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heisenberg-smooth operators from the phase space perspective Fulsche, Robert van Luijk, Lauritz Functional Analysis 47G30, 43A99 Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) We can admit general quantization schemes, (2) allow for other phase space geometries, (3) obtain Schatten class analogs of the result, and (4) are able to characterize precisely 'Heisenberg-analytic' operators. For (3), we use QHA to derive Schatten versions of the Calderón-Vaillancourt theorem, which might be of independent interest. |
| title | Heisenberg-smooth operators from the phase space perspective |
| topic | Functional Analysis 47G30, 43A99 |
| url | https://arxiv.org/abs/2410.00458 |