Non-Euclidean Fourier inversion on super-hyperbolic space
arXiv:1604.05029 · doi:10.1007/s00220-016-2804-7
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
30 pages; final version accepted for publication in Comm. Math. Phys