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<p>This paper investigates the application of the octonion-valued Fourier transform (OFT) for the analysis of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \mathbb {R}^3 \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> octonion signals. By exploiting the relationship between the OFT and the 3D quaternion Fourier transform (3D-QFT) and applying Miyachi’s theorem associated with the 3D-QFT, we present a generalized version of Miyachi’s theorem for the OFT. This generalization extends Miyachi’s theorem to include two variants in the OFT domain: Hardy’s and Cowling-Price uncertainty principles.</p>

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The Octonion-Valued Fourier Transform and Generalized Miyachi’s Theorem

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Youssef El Haoui,
  • Mohra Zayed

摘要

This paper investigates the application of the octonion-valued Fourier transform (OFT) for the analysis of \( \mathbb {R}^3 \) R 3 octonion signals. By exploiting the relationship between the OFT and the 3D quaternion Fourier transform (3D-QFT) and applying Miyachi’s theorem associated with the 3D-QFT, we present a generalized version of Miyachi’s theorem for the OFT. This generalization extends Miyachi’s theorem to include two variants in the OFT domain: Hardy’s and Cowling-Price uncertainty principles.