Hardy spaces on SU(2)
Harmonic analysis and Radon transforms on pencils of geodesics.
Harmonic analysis for spinors on real hyperbolic spaces
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...
Harmonic Analysis for Vector Fields on Hyperbolic Spaces.
Higher solutions of hypergeometric systems and Dwork cohomology