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<p>The generalized linear canonical wavelet transform (GLCWT) is a novel addition to the class of linear canonical wavelet transforms, which has gained recognition in the realm of harmonic analysis within a short span of time. Since the study of time-frequency analysis is both theoretically interesting and practically useful, this paper investigates several results related to the GLCWT. We introduce the localization operators associated with the GLCWT and prove its <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> boundedness and compactness. Then, we study their trace class properties and prove that they are in the Schatten–von Neumann classes. In addition, we explore the eigenvalues and eigenfunctions of the generalized concentration operator and present some results on the scalogram of the GLCWT. Finally, we investigate a few versions of the quantitative uncertainty principles for the GLCWT and some applications for the approximation theory.</p>

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Time-Frequency Analysis Associated with the Generalized Linear Canonical Wavelet Transform and Applications

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Hatem Mejjaoli,
  • Anirudha Poria

摘要

The generalized linear canonical wavelet transform (GLCWT) is a novel addition to the class of linear canonical wavelet transforms, which has gained recognition in the realm of harmonic analysis within a short span of time. Since the study of time-frequency analysis is both theoretically interesting and practically useful, this paper investigates several results related to the GLCWT. We introduce the localization operators associated with the GLCWT and prove its \(L^{p}\) L p boundedness and compactness. Then, we study their trace class properties and prove that they are in the Schatten–von Neumann classes. In addition, we explore the eigenvalues and eigenfunctions of the generalized concentration operator and present some results on the scalogram of the GLCWT. Finally, we investigate a few versions of the quantitative uncertainty principles for the GLCWT and some applications for the approximation theory.