<p>The Radon–Kipriyanov transformation (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7889_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$K_\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>γ</mi> </msub> </math></EquationSource> </InlineEquation>) was introduced in 1998. In theoretical and applied studies, it is necessary to introduce its dual transformation, which is denoted by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7889_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$K_\gamma ^{\#}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>K</mi> <mi>γ</mi> <mo>#</mo> </msubsup> </math></EquationSource> </InlineEquation> in this paper. Theorems on the boundedness of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7889_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$K_\gamma ^{\#}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>K</mi> <mi>γ</mi> <mo>#</mo> </msubsup> </math></EquationSource> </InlineEquation> transformation in the corresponding Schwartz subspace of the main functions are proved. A formula for representing the generalized convolution of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7889_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$K_\gamma ^{\#}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>K</mi> <mi>γ</mi> <mo>#</mo> </msubsup> </math></EquationSource> </InlineEquation>-transformations of functions belonging to the corresponding spaces of the main functions is obtained.</p>

DUAL RADON–KIPRIYANOV TRANSFORMATION. BASIC PROPERTIES

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

The Radon–Kipriyanov transformation ( $K_\gamma $ $K_{γ}$ ) was introduced in 1998. In theoretical and applied studies, it is necessary to introduce its dual transformation, which is denoted by $K_\gamma ^{\#}$ $K_{γ}^{#}$ in this paper. Theorems on the boundedness of the $K_\gamma ^{\#}$ $K_{γ}^{#}$ transformation in the corresponding Schwartz subspace of the main functions are proved. A formula for representing the generalized convolution of $K_\gamma ^{\#}$ $K_{γ}^{#}$ -transformations of functions belonging to the corresponding spaces of the main functions is obtained.