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Harmonic analysis for spinors on real hyperbolic spaces

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Camporesi R., Pedon E.

Colloquium Mathematicum

2001

tom 87

nr 2

245-286

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Camporesi R.

1 Pedon E.

1 2001

Wyniki wyszukiwania

Harmonic analysis for spinors on real hyperbolic spaces