A representation formula for regular functions on the characteristic plane of the second Heisenberg group
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909372735553536 |
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| author | Baldi, Annalisa Citti, Giovanna Cupini, Giovanni |
| author_facet | Baldi, Annalisa Citti, Giovanna Cupini, Giovanni |
| contents | The aim of this paper is to study a Laplace-type operator and its fundamental solution on the characteristic plane in the Heisenberg group $\mathbb{H}^2$. We introduce a conformal version of the Laplacian and we prove that the distance induced by the immersion in the ambient space is a good approximation of its fundamental solution. We provide in particular a representation formula for smooth functions in terms of the gradient of the function and the gradient of the approximated fundamental solution. This representation formula in the plane is stable up to its characteristic point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A representation formula for regular functions on the characteristic plane of the second Heisenberg group Baldi, Annalisa Citti, Giovanna Cupini, Giovanni Analysis of PDEs 35R03, 35A08, 35B65, 31B10 The aim of this paper is to study a Laplace-type operator and its fundamental solution on the characteristic plane in the Heisenberg group $\mathbb{H}^2$. We introduce a conformal version of the Laplacian and we prove that the distance induced by the immersion in the ambient space is a good approximation of its fundamental solution. We provide in particular a representation formula for smooth functions in terms of the gradient of the function and the gradient of the approximated fundamental solution. This representation formula in the plane is stable up to its characteristic point. |
| title | A representation formula for regular functions on the characteristic plane of the second Heisenberg group |
| topic | Analysis of PDEs 35R03, 35A08, 35B65, 31B10 |
| url | https://arxiv.org/abs/2410.23256 |