We develop the L² harmonic analysis for (Dirac) spinors on the real hyperbolic space Hⁿ(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 L²(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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-10,
author = {Roberto Camporesi and Emmanuel Pedon},
title = {Harmonic analysis for spinors on real hyperbolic spaces},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {245-286},
zbl = {0968.22009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-10}
}
Roberto Camporesi; Emmanuel Pedon. Harmonic analysis for spinors on real hyperbolic spaces. Colloquium Mathematicae, Tome 89 (2001) pp. 245-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-10/