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<p>Starting from the study of pseudodifferential operators with completely periodic symbols, we obtain results of continuity and invertibility of a class of Gabor operators on time-frequency invariant Banach spaces. As an application, we find sufficient conditions for the existence of Gabor frames on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>, associated with a general lattice <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L {\mathbb {Z}}^{2d}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, where <i>L</i> is an invertible square matrix.</p>

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Pseudodifferential operators on time-frequency invariant Banach spaces and applications to Gabor Frames

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月25日

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  • Gianluca Garello,
  • Alessandro Morando

摘要

Starting from the study of pseudodifferential operators with completely periodic symbols, we obtain results of continuity and invertibility of a class of Gabor operators on time-frequency invariant Banach spaces. As an application, we find sufficient conditions for the existence of Gabor frames on \(L^2\) L 2 , associated with a general lattice \(L {\mathbb {Z}}^{2d}\) L Z 2 d , where L is an invertible square matrix.