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The k-plane transform on the Heisenberg group

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Abstract

The paper deals with the k-plane transform \({\mathcal {R}}_{k}\) on the Heisenberg group. We study the properties of the transform \({\mathcal {R}}_{k}\) and obtain three types of inversion formulas for \({\mathcal {R}}_{k}\). The first inversion is deduced with the help of the group Fourier transform, together with the partial Riesz potential and Heisenberg sublaplacian. By this formula, another two formulas are established in terms with the adjoint of \({\mathcal {R}}_{k}\) and the wavelet, respectively.

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Acknowledgements

The work for this paper is supported by the National Natural Science Foundation of China (Nos. 11501131, 11671414) and Guangdong Basic and Applied Basic Research Foundation (2019A1515010955).

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Correspondence to Jianxun He.

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Xiao, J., He, J. The k-plane transform on the Heisenberg group. J. Pseudo-Differ. Oper. Appl. 11, 289–309 (2020). https://doi.org/10.1007/s11868-019-00314-1

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Keywords

  • k-plane transform
  • Radon transform
  • Heisenberg group
  • Inversion formula
  • Riesz potential

Mathematics Subject Classification

  • 43A85
  • 44A12