The k-plane transform on the Heisenberg group

The paper deals with the k -plane transform R k on the Heisenberg group. We study the properties of the transform R k and obtain three types of inversion formulas for R k . The first inversion is deduced with the help of the group Fourier transform, together with the partial Riesz potential and Heis...

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Bibliographic Details
Published in:Journal of pseudo-differential operators and applications 2020-03, Vol.11 (1), p.289-309
Main Authors: Xiao, Jinsen, He, Jianxun
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Fourier transforms
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
Wavelet analysis
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Summary:The paper deals with the k -plane transform R k on the Heisenberg group. We study the properties of the transform R k and obtain three types of inversion formulas for 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 R k and the wavelet, respectively.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-019-00314-1