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arXiv · 2309.10685

Analytic Wavefront Sets of Spherical Distributions on De Sitter Space

Gestur Olafsson·Iswarya Sitiraju
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Abstract

In this article we determine the wavefront sets of spherical distributions on the de Sitter space dS = G/H, G= SO_{1,n}(R)_e. These are eigendistributions of the Laplacian on dS = G/H invariant under the subgroup H. We construct bases for the spaces of spherical distributions as boundary values of sesquiholomorphic kernels on a certain G-invariant complex domain in dS^n_C containing the de Sitter space as a G-orbit on the boundary. We characterize the elements of the basis by their analytic wavefront sets. We also treat the spherical distributions invariant under O_{1,n-1}(R).

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Gestur Olafsson, Iswarya Sitiraju. 2023-09-19. Analytic Wavefront Sets of Spherical Distributions on De Sitter Space. https://arxiv.org/abs/2309.10685

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