Lieb–Thirring inequalities on the spheres and SO(3)

IF 1.4 3区 数学 Q1 MATHEMATICS
André Kowacs, Michael Ruzhansky
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引用次数: 0

Abstract

In this paper, we obtain new upper bounds for the Lieb–Thirring inequality on the spheres of any dimension greater than 2. As far as we have checked, our results improve previous results found in the literature for all dimensions greater than 2. We also prove and exhibit an explicit new upper bound for the Lieb–Thirring inequality on SO(3). We also discuss these estimates in the case of general compact Lie groups. Originally developed for estimating the sums of moments of negative eigenvalues of the Schrödinger operator in \(L^2(\mathbb {R}^n)\), these inequalities have applications in quantum mechanics and other fields.

球面和 SO(3) 上的李卜-蒂林不等式
在本文中,我们获得了任何维数大于 2 的球面上李卜-特林不等式的新上限。我们还证明并展示了 SO(3) 上 Lieb-Thirring 不等式的明确新上限。我们还讨论了在一般紧凑李群情况下的这些估计值。这些不等式最初是为了估计薛定谔算子在\(L^2(\mathbb {R}^n)\)中负特征值的矩之和而开发的,在量子力学和其他领域都有应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Analysis and Mathematical Physics
Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.70
自引率
0.00%
发文量
122
期刊介绍: Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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