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<p>We provide a growth bound for the operator norm of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="233_2025_10549_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 under a corresponding growth bound on the resolvent of the semigroup generator. For some super-linear resolvent growths, our estimate is sharper than the ones currently available in the literature.</p>

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A remark on the growth rate of operator semigroups under resolvent bounds

  • 期刊论文

  • 发表日期：

    2025年6月30日

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  • Filippo Dell’Oro

摘要

We provide a growth bound for the operator norm of \(C_0\) C 0 -semigroups on Hilbert spaces under a corresponding growth bound on the resolvent of the semigroup generator. For some super-linear resolvent growths, our estimate is sharper than the ones currently available in the literature.