The Radon–Kipriyanov transform of the generalized spherical mean of a function

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• 作者：L. N. Lyakhov
• 关键词：Radon transform ; Radon–Kipriyanov transform ; radial function ; multiaxial spherical symmetry ; generalized spherical mean ; fractional integral ; fractional derivative
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：100
• 期：1-2
• 页码：100-112
• 全文大小：771 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876
• 卷排序：100

文摘

A formula relating the Radon transform of functions of spherical symmetries to the Radon–Kipriyanov transform K_γ for a naturalmulti-index γ is given. For an arbitrary multi-index γ, formulas for the representation of the K_γ-transform of a radial function as fractional integrals of Erdelyi–Kober integral type and of Riemann–Liouville integral type are proved. The corresponding inversion formulas are obtained. These results are used to study the inversion of the Radon–Kipriyanov transform of the generalized (generated by a generalized shift) spherical mean values of functions that belong to a weighted Lebesgue space and are even with respect to each of the weight variables.