The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916019178569728 |
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| author | Cornean, Horia D. Helffer, Bernard Purice, Radu |
| author_facet | Cornean, Horia D. Helffer, Bernard Purice, Radu |
| contents | We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen as operators on the $d$-dimensional torus, and also when they are seen as infinite matrices acting on a discrete $\ell^2$ space via a discrete Fourier transform. Moreover, using these distribution kernels we prove that the fibre operators are toroidal pseudo-differential operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators Cornean, Horia D. Helffer, Bernard Purice, Radu Analysis of PDEs 35S05, 47G30, 43A70, 81S99 We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen as operators on the $d$-dimensional torus, and also when they are seen as infinite matrices acting on a discrete $\ell^2$ space via a discrete Fourier transform. Moreover, using these distribution kernels we prove that the fibre operators are toroidal pseudo-differential operators. |
| title | The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators |
| topic | Analysis of PDEs 35S05, 47G30, 43A70, 81S99 |
| url | https://arxiv.org/abs/2512.22547 |