Harmonic analysis for spinors on real hyperbolic spaces

Volume 87 / 2001

Roberto Camporesi, Emmanuel Pedon Colloquium Mathematicum 87 (2001), 245-286 MSC: 22E30, 22E46, 33C80, 43A85, 43A90. DOI: 10.4064/cm87-2-10


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.


  • Roberto CamporesiDipartimento di Matematica
    Politecnico di Torino
    Corso Duca degli Abruzzi, 24
    10129 Torino, Italy
  • Emmanuel PedonLaboratoire de Mathématiques
    Université de Reims
    Moulin de la Housse, B.P. 1039
    51687 Reims Cedex 2, France

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