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<p>In this paper, we introduce the three-dimensional octonionic hyperbolic linear canonical transform (OHLCT). We investigate its fundamental properties, including linearity, scaling, reflection, boundedness, the Riemann–Lebesgue lemma, the inversion formula and Plancherel’s theorem. Furthermore, we extend the Heisenberg–Weyl uncertainty principle to the OHLCT domain and provide illustrative examples to verify its validity. In addition, we derive analogues of the Hausdorff–Young inequality and the Matolcsi–Szücs uncertainty principle within the framework of the OHLCT.</p>

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Uncertainty principles for the hyperbolic linear canonical transform of octonion-valued functions

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Khaled Hleili,
  • Manel Hleili

摘要

In this paper, we introduce the three-dimensional octonionic hyperbolic linear canonical transform (OHLCT). We investigate its fundamental properties, including linearity, scaling, reflection, boundedness, the Riemann–Lebesgue lemma, the inversion formula and Plancherel’s theorem. Furthermore, we extend the Heisenberg–Weyl uncertainty principle to the OHLCT domain and provide illustrative examples to verify its validity. In addition, we derive analogues of the Hausdorff–Young inequality and the Matolcsi–Szücs uncertainty principle within the framework of the OHLCT.