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<p>The present work is devoted to the study of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_942_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathbb {R}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>-analyticity with respect to the set of variables of separately <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_942_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathbb {R}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>-analytic functions. In the paper, it is proved real analyticity with respect to the set of variables, out of some pluripolar set, of the separately <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_942_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathbb {R}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>-analytic functions.</p>

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Cross theorem for separately real-analytic functions

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Atamuratov Alimardon,
  • Rasulov Kamol

摘要

The present work is devoted to the study of \({{\mathbb {R}}}\) R -analyticity with respect to the set of variables of separately \({{\mathbb {R}}}\) R -analytic functions. In the paper, it is proved real analyticity with respect to the set of variables, out of some pluripolar set, of the separately \({{\mathbb {R}}}\) R -analytic functions.