Harmonic analysis for spinors on real hyperbolic spaces

Roberto Camporesi¹ ; Emmanuel Pedon²

¹ Dipartimento di Matematica Politecnico di Torino Corso Duca degli Abruzzi, 24 10129 Torino, Italy
² Laboratoire de Mathématiques Université de Reims Moulin de la Housse, B.P. 1039 51687 Reims Cedex 2, France

Colloquium Mathematicum, Tome 87 (2001) no. 2, pp. 245-286.

Résumé

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.

Détail

DOI : 10.4064/cm87-2-10

Keywords: develop harmonic analysis dirac spinors real hyperbolic space mathbb analogue classical notions results known functions differential forms investigate poisson transform spherical function theory spherical fourier transform fourier transform explicit expressions statements obtained reduction jacobi analysis mathbb applications describe exact spectrum dirac operator study abel transform derive explicit expressions heat kernel associated spinor laplacian