Abstract

Here we consider the Heisenberg group H_n = Cⁿ ×R. U, p + q = n, acts by automorphism on H_n by g • = .

Let be the standard basis of the Lie algebra of H_n and let

Via the Plancherel inversion formula, we obtain the joint spectral decomposition of L² with respect to L and T

where each S_λ.k is a tempered distribution U invariant satisfying iTS_λ,k = λS_λ,k, LS_λ,k = −S_λ,k. We compute explicitly the distributions S_λ,k and the integral μ_k = ∫ _−∞^+∞f * S_λ,kⁿdλ.

Authors