Harmonic analysis for spinors on real hyperbolic spaces

• Autorzy: Roberto Camporesi , Emmanuel Pedon
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 43A90: Spherical functions
• 22E46: Semisimple Lie groups and their representations
• 33C80: Connections with groups and algebras, and related topics
• 43A85: Analysis on homogeneous spaces
• 22E30: Analysis on real and complex Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 87
• Numer: 2
• Strony: 245-286

Daty

wydano

2001

Twórcy

autor

Roberto Camporesi

• Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

autor

Emmanuel Pedon

• Laboratoire de Mathématiques, Université de Reims, Moulin de la Housse, B.P. 1039, 51687 Reims Cedex 2, France

Identyfikatory

DOI

10.4064/cm87-2-10