Analytic Wavefront Sets of Spherical Distributions on the De Sitter Space

Author

Iswarya Sitiraju, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this work, we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G′ = O_1,n(R) be the Lorentz group, and let H′ = O_1,n−1(R) ⊂ G′ be its subset. The de Sitter space dSⁿ is a one-sheeted hyperboloid in R^1,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 D_λ^H'(dSⁿ), has dimension 2. We construct a basis for the space of positive-definite spherical distributions as boundary value of sesquiholomorphic kernels on the crown domains, which are open complex domains in dSⁿ_C containing dSⁿ on the boundary. We characterize the analytic wavefront set for such distributions.

Date

4-4-2024

Recommended Citation

Sitiraju, Iswarya, "Analytic Wavefront Sets of Spherical Distributions on the De Sitter Space" (2024). LSU Doctoral Dissertations. 6426.
https://repository.lsu.edu/gradschool_dissertations/6426

Committee Chair

Gestur Olafsson