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<p>In this article, we investigate some important theoretical aspects of the deformed wavelet transform, which is a novel variant of the wavelet transform based on generalized translation and dilation operators governed by the well-known Dunkl transform. Besides studying all the fundamental properties, we establish the Calderón’s and inversion formulae associated with the newly proposed transform. Most importantly, we formulate a new class of localization operators associated with the deformed wavelet transform and examine the <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 properties of such operators in detail.</p>

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Localization operators in the realm of deformed wavelet transform

  • 期刊论文

  • 发表日期：

    2025年2月4日

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  • Hatem Mejjaoli,
  • Firdous A. Shah,
  • Nadia Sraieb

摘要

In this article, we investigate some important theoretical aspects of the deformed wavelet transform, which is a novel variant of the wavelet transform based on generalized translation and dilation operators governed by the well-known Dunkl transform. Besides studying all the fundamental properties, we establish the Calderón’s and inversion formulae associated with the newly proposed transform. Most importantly, we formulate a new class of localization operators associated with the deformed wavelet transform and examine the \(L^p\) L p -boundedness and compactness properties of such operators in detail.