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An inversion formula of Radon transform on the product Heisenberg group. (English) Zbl 1248.43006

Let \(H^n_1\) be the \(n-\)direct product of the Heisenberg groups \(H_1\). This paper gives the definitions of the wavelet transform and the Radon transform, then it gives the direct sum decomposition of \(L^2(H^n_1)\) and presents the inversion of the Radon transform on \(H^n_1\) by using inverse wavelet transform. In addition, it characterizes a subspace such that the inversion formula holds in the weak sense.

MSC:

43A85 Harmonic analysis on homogeneous spaces
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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References:

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