Geodesic
Harmonic analysis for spinors on real hyperbolic spaces
Roberto Camporesi 1   ; Emmanuel Pedon 2
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
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

Roberto Camporesi  1   ; Emmanuel Pedon  2

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 
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Roberto Camporesi; Emmanuel Pedon. Harmonic analysis for spinors
on real hyperbolic spaces. Colloquium Mathematicum, Tome 87 (2001) no. 2, pp. 245-286. doi: 10.4064/cm87-2-10

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