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arXiv · 1604.05029

Non-Euclidean Fourier inversion on super-hyperbolic space

Alexander Alldridge·Wolfgang Palzer
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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

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Alexander Alldridge, Wolfgang Palzer. 2016-04-18. Non-Euclidean Fourier inversion on super-hyperbolic space. https://doi.org/10.1007/s00220-016-2804-7

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