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<p>This paper introduces the fractional Lions transform, a new integral transform. We investigate its fundamental properties and derive both the inversion and Parseval formulas. In addition, we define the associated translation operators and convolution product, examining their key properties. Building on these foundations, we develop the continuous fractional Lions wavelet transform and establish several related inequalities. Finally, we introduce the localization operators associated with the fractional Lions wavelet transform and study their boundedness.</p>

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The fractional Lions transform and its associated wavelet analysis

  • 期刊论文

  • 发表日期：

    2026年1月18日

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  • Nabiha Ben Abdallah

摘要

This paper introduces the fractional Lions transform, a new integral transform. We investigate its fundamental properties and derive both the inversion and Parseval formulas. In addition, we define the associated translation operators and convolution product, examining their key properties. Building on these foundations, we develop the continuous fractional Lions wavelet transform and establish several related inequalities. Finally, we introduce the localization operators associated with the fractional Lions wavelet transform and study their boundedness.