Non-Euclidean Fourier inversion on super-hyperbolic space
Representation Theory
2017-10-05 v2 Mathematical Physics
math.MP
Abstract
For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason--Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary terms appearing in the polar coordinate expression of the invariant integral
Cite
@article{arxiv.1604.05029,
title = {Non-Euclidean Fourier inversion on super-hyperbolic space},
author = {Alexander Alldridge and Wolfgang Palzer},
journal= {arXiv preprint arXiv:1604.05029},
year = {2017}
}
Comments
30 pages; final version accepted for publication in Comm. Math. Phys