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Abstract

We calculate the group Fourier transform of regular homogeneous distributions defined on the Heisenberg group, $H^n$. All such distributions can be written as an infinite sum of terms of the form $f(θ)\overline{w}^{-k}P(z)$, where $(z,t) ∈ ℂ^{n} × ℝ$, $w = |z|^2 - it$, $θ = arg(\overline{w/w)$ and P(z) is an element of an orthonormal basis for the spherical harmonics. The formulas derived give the Fourier transform of the distribution in terms of a smooth kernel of the variable θ and the Weyl correspondent of P.