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Abstract <p>A new formula for the inversion of the Radon–Kipriyanov transform for the multidimensional case is obtained. Result based on the introduction of the dual Radon–Kipriyanov transform and the inversion of the classical one-dimensional Riesz potential using the one-dimensional Fourier transform. A formula for the transformation of a linear singular partial differential operator into an ordinary (and non-singular) differential operator is proved. The formula is obtained by applying the Radon–Kipriyanov transform to a singular partial differential operator.</p>

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On Solutions of Singular Differential Equations Based on the Formula for the Inversion of the Radon–Kipriyanov Transform

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • L. N. Lyakhov,
  • V. A. Kalitvin,
  • M. G. Lapshina

摘要

Abstract

A new formula for the inversion of the Radon–Kipriyanov transform for the multidimensional case is obtained. Result based on the introduction of the dual Radon–Kipriyanov transform and the inversion of the classical one-dimensional Riesz potential using the one-dimensional Fourier transform. A formula for the transformation of a linear singular partial differential operator into an ordinary (and non-singular) differential operator is proved. The formula is obtained by applying the Radon–Kipriyanov transform to a singular partial differential operator.