1Dipartimento di Matematica Politecnico di Torino Corso Duca degli Abruzzi, 24 10129 Torino, Italy 2Laboratoire 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
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.
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
Affiliations des auteurs :
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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author = {Roberto Camporesi and Emmanuel Pedon},
title = {Harmonic analysis for spinors
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AU - Emmanuel Pedon
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on real hyperbolic spaces
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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
