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<p>We show that under certain inequality assumptions an arbitrary linear operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10_2025_1158_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="141" /> </InlineMediaObject> <EquationSource Format="TEX">\(D:C^\infty (\mathbb {R}) \rightarrow C(\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>D</mi> <mo>:</mo> <msup> <mi>C</mi> <mi>∞</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">→</mo> <mi>C</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is a differential operator, for example, if <i>D</i>[<i>f</i>] is nonnegative in local minima of <i>f</i>.</p>

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Inequalities characterizing differential operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月16日

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  • Gerd Herzog,
  • Peer Kunstmann

摘要

We show that under certain inequality assumptions an arbitrary linear operator \(D:C^\infty (\mathbb {R}) \rightarrow C(\mathbb {R})\) D : C ∞ ( R ) → C ( R ) is a differential operator, for example, if D[f] is nonnegative in local minima of f.