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<p>In the present paper, we define the linear canonical wavelets and study the corresponding wavelet transforms along with some valuable properties and outcomes for it. Parseval’s identity, reconstruction formula for linear canonical wavelet transform are obtained. Weyl transform to the admissible linear canonical wavelet space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \mathfrak {W} \)</EquationSource> </InlineEquation> is proposed and boundedness as well as compactness of Weyl transform in Lebesgue space are discussed. Some potential applications of the proposed transform are also discussed to demonstrate its usefulness.</p>

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Weyl transform associated with linear canonical wavelets

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Akhilesh Prasad,
  • Amit Kumar

摘要

In the present paper, we define the linear canonical wavelets and study the corresponding wavelet transforms along with some valuable properties and outcomes for it. Parseval’s identity, reconstruction formula for linear canonical wavelet transform are obtained. Weyl transform to the admissible linear canonical wavelet space \( \mathfrak {W} \) is proposed and boundedness as well as compactness of Weyl transform in Lebesgue space are discussed. Some potential applications of the proposed transform are also discussed to demonstrate its usefulness.