<p>In this paper, we consider the Linear Canonical Bessel operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2024_1144_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta _{B,\alpha }^{\mathcal {A}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow> <mi>B</mi> <mo>,</mo> <mi>α</mi> </mrow> <mi mathvariant="script">A</mi> </msubsup> </math></EquationSource> </InlineEquation>, we introduce and study the continuous Linear Canonical Bessel Gabor Transform denoted by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2024_1144_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathscr {G}_{g}^{\mathcal {a}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">G</mi> <mrow> <mi>g</mi> </mrow> <mi mathvariant="script">a</mi> </msubsup> </math></EquationSource> </InlineEquation> associated with the operator <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2024_1144_Article_IEq3.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta _{B,\alpha }^{\mathcal {A}}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow> <mi>B</mi> <mo>,</mo> <mi>α</mi> </mrow> <mi mathvariant="script">A</mi> </msubsup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> We prove a Plancherel formula and a weak uncertainty principle for it. We obtain analogous of Heisenbeg’s inequality for the Linear Canonical Bessel Gabor Transform.</p>

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Linear canonical bessel gabor transform

  • Hassen Ben Mohamed,
  • Nahed Krir

摘要

In this paper, we consider the Linear Canonical Bessel operator \(\Delta _{B,\alpha }^{\mathcal {A}}\) Δ B , α A , we introduce and study the continuous Linear Canonical Bessel Gabor Transform denoted by \(\mathscr {G}_{g}^{\mathcal {a}}\) G g a associated with the operator \(\Delta _{B,\alpha }^{\mathcal {A}}.\) Δ B , α A . We prove a Plancherel formula and a weak uncertainty principle for it. We obtain analogous of Heisenbeg’s inequality for the Linear Canonical Bessel Gabor Transform.