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<p>The <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1657_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroups for the weighted composition operators on the Hardy spaces of Dirichlet series are completely characterized in this paper. This generalizes previous results in a recent paper of Contreras et al. regarding <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1657_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroup of (unweighted) composition operators. As applications, we calculate the infinitesimal generator of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1657_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroups and its point spectrum.</p>

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Semigroups of Weighted Composition Operators on Hardy Spaces of Dirichlet Series

  • 期刊论文

  • 发表日期：

    2025年1月21日

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  • Chengshi Huang,
  • Maofa Wang,
  • Xingxing Yao

摘要

The \(C_{0}\) C 0 -semigroups for the weighted composition operators on the Hardy spaces of Dirichlet series are completely characterized in this paper. This generalizes previous results in a recent paper of Contreras et al. regarding \(C_{0}\) C 0 -semigroup of (unweighted) composition operators. As applications, we calculate the infinitesimal generator of the \(C_{0}\) C 0 -semigroups and its point spectrum.