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<p>In this article, we investigate sharp functional inequalities associated with the coherent state transforms of the Lie group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( SU(N,1) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mi>N</mi> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Assuming the isoperimetric conjecture on the complex hyperbolic ball, we establish the Lieb–Wehrl entropy conjecture for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( SU(N,1) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mi>N</mi> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( N \ge 2 \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. Furthermore, we derive an extension of the Faber–Krahn type inequality within the framework of the Bergman space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( \mathcal {A}_{\alpha } \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">A</mi> <mi>α</mi> </msub> </math></EquationSource> </InlineEquation>.</p>

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On the Lieb–Wehrl Entropy conjecture for SU(N, 1)

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Mandeep Singh

摘要

In this article, we investigate sharp functional inequalities associated with the coherent state transforms of the Lie group \( SU(N,1) \) S U ( N , 1 ) . Assuming the isoperimetric conjecture on the complex hyperbolic ball, we establish the Lieb–Wehrl entropy conjecture for \( SU(N,1) \) S U ( N , 1 ) with \( N \ge 2 \) N ≥ 2 . Furthermore, we derive an extension of the Faber–Krahn type inequality within the framework of the Bergman space \( \mathcal {A}_{\alpha } \) A α .