Harmonic analysis for spinors on real hyperbolic spaces

Roberto Camporesi, Emmanuel Pedon
2001 Colloquium Mathematicum  
We develop the L 2 harmonic analysis for (Dirac) spinors on the real hyperbolic space H n (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 (R). As applications, we describe the exact spectrum of the Dirac operator, study the Abel
more » ... , study the Abel transform and derive explicit expressions for the heat kernel associated with the spinor Laplacian.
doi:10.4064/cm87-2-10 fatcat:6wgukk3exzclzemf2kctbgirma