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<p>In this work, using the quaternion linear canonical transform, we establish an analogue of the classical Titchmarsh theorem and Younis’ theorem for higher-order differences of quaternion-valued functions satisfying certain Lipschitz conditions in the space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( L^{2}( {\mathbb {R}}^{2},{\mathbb {H}}),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo>,</mo> <mi mathvariant="double-struck">H</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathbb {H}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation> is a quaternion algebra.</p>

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Characterizations of Lipschitz Functions by Quaternion Linear Canonical Transform

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Monir Nadi,
  • El Mostafa Sadek,
  • Hassan Benlaajine

摘要

In this work, using the quaternion linear canonical transform, we establish an analogue of the classical Titchmarsh theorem and Younis’ theorem for higher-order differences of quaternion-valued functions satisfying certain Lipschitz conditions in the space \( L^{2}( {\mathbb {R}}^{2},{\mathbb {H}}),\) L 2 ( R 2 , H ) , where \({\mathbb {H}}\) H is a quaternion algebra.