Harmonic analysis for spinors on real hyperbolic spaces

Roberto Camporesi; Emmanuel Pedon

Colloquium Mathematicae (2001)

  • Volume: 87, Issue: 2, page 245-286
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Roberto Camporesi, and Emmanuel Pedon. "Harmonic analysis for spinors on real hyperbolic spaces." Colloquium Mathematicae 87.2 (2001): 245-286. <http://eudml.org/doc/284346>.

@article{RobertoCamporesi2001,
abstract = {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.},
author = {Roberto Camporesi, Emmanuel Pedon},
journal = {Colloquium Mathematicae},
keywords = {hyperbolic spaces; spinors; Dirac operator; spherical functions; Jacobi functions; Fourier transform; Abel transform; heat kernel},
language = {eng},
number = {2},
pages = {245-286},
title = {Harmonic analysis for spinors on real hyperbolic spaces},
url = {http://eudml.org/doc/284346},
volume = {87},
year = {2001},
}

TY - JOUR
AU - Roberto Camporesi
AU - Emmanuel Pedon
TI - Harmonic analysis for spinors on real hyperbolic spaces
JO - Colloquium Mathematicae
PY - 2001
VL - 87
IS - 2
SP - 245
EP - 286
AB - 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.
LA - eng
KW - hyperbolic spaces; spinors; Dirac operator; spherical functions; Jacobi functions; Fourier transform; Abel transform; heat kernel
UR - http://eudml.org/doc/284346
ER -

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