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<p>In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1271_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.</p>

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Toeplitz operators associated with the directional short-time Fourier transform and applications

  • 期刊论文

  • 发表日期：

    2025年1月20日

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  • Saifallah Ghobber,
  • Hatem Mejjaoli,
  • Slim Omri

摘要

In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the \(L^{p}\) L p -spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.