Harmonic analysis for spinors on real hyperbolic spaces
Volume 87 / 2001
Colloquium Mathematicum 87 (2001), 245-286
MSC: 22E30, 22E46, 33C80, 43A85, 43A90.
DOI: 10.4064/cm87-2-10
Abstract
We develop the $L^2$ harmonic analysis for (Dirac) spinors on the real hyperbolic space $H^n({\mathbb R})$ and give the analogue of the classical notions and results known for functions and differential forms: we investigate the Poisson transform, spherical function theory, spherical Fourier transform and Fourier transform. Very explicit expressions and statements are obtained by reduction to Jacobi analysis on $L^2({\mathbb R})$. As applications, we describe the exact spectrum of the Dirac operator, study the Abel transform and derive explicit expressions for the heat kernel associated with the spinor Laplacian.
