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Analytic Wavefront Sets Of Spherical Distributions On The De Sitter Space, Iswarya Sitiraju
Analytic Wavefront Sets Of Spherical Distributions On The De Sitter Space, Iswarya Sitiraju
LSU Doctoral Dissertations
In this work, we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G′ = O1,n(R) be the Lorentz group, and let H′ = O1,n−1(R) ⊂ G′ be its subset. The de Sitter space dSn is a one-sheeted hyperboloid in R1,n isomorphic to G′/H′. A spherical distribution is an H′-invariant eigendistribution of the Laplace-Beltrami operator on dSn. The space of spherical distributions with eigenvalue λ, denoted by DλH'(dSn), has dimension 2. We construct a basis for the space of …