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Harmonic analysis for spinors on real hyperbolic spaces

Roberto Camporesi;  Emmanuel Pedon — 2001

Colloquium Mathematicae

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...

On the differential form spectrum of hyperbolic manifolds

Gilles Carron;  Emmanuel Pedon — 2004

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We give a lower bound for the bottom of the L 2 differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodge-de Rham laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds.

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