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<p>In this paper, we provide an alternative proof of the Gearhart-Prüss theorem for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2517_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 on Hilbert spaces. The approach relies on a characterization of the uniform exponential stability via an estimate of a tempered distribution defined in terms of the resolvent.</p>

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Alternative Proof of the Gearhart-Prüss Theorem

  • 期刊论文

  • 发表日期：

    2025年9月16日

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  • Abdelhadi El Harfi

摘要

In this paper, we provide an alternative proof of the Gearhart-Prüss theorem for \(C_0\) C 0 -semigroups on Hilbert spaces. The approach relies on a characterization of the uniform exponential stability via an estimate of a tempered distribution defined in terms of the resolvent.