Scholarlink

<p>The Fourier exchange theorem according to Y.&#xa0;Hirata and H.&#xa0;Ogata says that if <i>S</i>,&#xa0;<i>T</i> are two temperate distributions that are <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {S}'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="script">S</mi> </mrow> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>-convolvable, then their Fourier transforms are multiplicable and fulfill <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {F}(S*T)=\mathcal {F}S\cdot \mathcal {F} T.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">F</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mrow /> <mo>∗</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="script">F</mi> <mi>S</mi> <mo>·</mo> <mi mathvariant="script">F</mi> <mi>T</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> This implication is sharpened to an equivalence by modifying the concepts of convolvability and multiplicability.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Fourier exchange theorems for temperate distributions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月3日

查看全文
  • Norbert Ortner,
  • Peter Wagner

摘要

The Fourier exchange theorem according to Y. Hirata and H. Ogata says that if S, T are two temperate distributions that are \(\mathcal {S}'\) S ′ -convolvable, then their Fourier transforms are multiplicable and fulfill \(\mathcal {F}(S*T)=\mathcal {F}S\cdot \mathcal {F} T.\) F ( S ∗ T ) = F S · F T . This implication is sharpened to an equivalence by modifying the concepts of convolvability and multiplicability.