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<p>The study of the Radon transform based on weighted plane waves was initiated by I.&#xa0;A.&#xa0;Kipriyanov. In this paper, we obtain necessary and sufficient conditions satisfied by the Radon <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(K_\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>γ</mi> </msub> </math></EquationSource> </InlineEquation>-transform of smooth functions that decrease together with all their derivatives.</p>

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AN ANALOG OF THE PALEY–WIENER THEOREM FOR THE RADON \(K_\gamma \)-TRANSFORM FOR INTEGER \(|\gamma |\)

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • L. N. Lyakhov,
  • M. G. Lapshina

摘要

The study of the Radon transform based on weighted plane waves was initiated by I. A. Kipriyanov. In this paper, we obtain necessary and sufficient conditions satisfied by the Radon \(K_\gamma \) K γ -transform of smooth functions that decrease together with all their derivatives.