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, the spherical function theory, the spherical Fourier transform and the 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 transform and derive explicit expressions for the heat kernel associated with the spinor Laplacian
Publié le : 2001-07-05
Classification:
Hyperbolic spaces,
Spinors,
Dirac operator,
Spherical functions,
Jacobi functions,
Fourier transform,
Abel transform,
Heat kernel,
MSC 22E30, 33C80, 43A85, 53A50,
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]
@article{hal-00160423,
author = {Pedon, Emmanuel and Camporesi, Roberto},
title = {Harmonic analysis for spinors on real hyperbolic spaces},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00160423}
}
Pedon, Emmanuel; Camporesi, Roberto. Harmonic analysis for spinors on real hyperbolic spaces. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00160423/