Spherical Distributions on the De Sitter Space and their Spectral Singularities
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910512502013952 |
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| author | Sitiraju, Iswarya |
| author_facet | Sitiraju, Iswarya |
| contents | A spherical distribution is an eigendistribution of the Laplace-Beltrami operator with certain invariance on the de Sitter space. Let G'=O(1,n;R) be the Lorentz group and H' = O(1,n-1;R) be its subgroup. The authors Olafsson and Sitiraju have constructed the spherical distributions, which are $H'$-invariant, as boundary values of some sesquiholomorphic kernels. In this survey article we will explore the connections of these kernels with reflection positivity and representations of the group G = SO(1,n;R)_e, which is the connected component of the Lorentz group. We will also discuss the singularities of spherical distributions in terms of their wavefront set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical Distributions on the De Sitter Space and their Spectral Singularities Sitiraju, Iswarya Functional Analysis 22F30, 43A85, 43A90, 46F20, 35A18 A spherical distribution is an eigendistribution of the Laplace-Beltrami operator with certain invariance on the de Sitter space. Let G'=O(1,n;R) be the Lorentz group and H' = O(1,n-1;R) be its subgroup. The authors Olafsson and Sitiraju have constructed the spherical distributions, which are $H'$-invariant, as boundary values of some sesquiholomorphic kernels. In this survey article we will explore the connections of these kernels with reflection positivity and representations of the group G = SO(1,n;R)_e, which is the connected component of the Lorentz group. We will also discuss the singularities of spherical distributions in terms of their wavefront set. |
| title | Spherical Distributions on the De Sitter Space and their Spectral Singularities |
| topic | Functional Analysis 22F30, 43A85, 43A90, 46F20, 35A18 |
| url | https://arxiv.org/abs/2407.03366 |