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<p>Let <i>G</i> be a connected, simply connected nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for oblique duals associated with shift-generated systems in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( L^2(G).\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> As a consequence of our results for the Heisenberg group, a reproducing formula associated with the orthonormal Gabor systems of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2(\mathbb {R}^d)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is obtained.</p>

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Shift-generated dual frames on a class of nilpotent Lie groups

  • 期刊论文

  • 发表日期：

    2026年4月2日

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  • Sudipta Sarkar,
  • Niraj K. Shukla

摘要

Let G be a connected, simply connected nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for oblique duals associated with shift-generated systems in \( L^2(G).\) L 2 ( G ) . As a consequence of our results for the Heisenberg group, a reproducing formula associated with the orthonormal Gabor systems of \(L^2(\mathbb {R}^d)\) L 2 ( R d ) is obtained.