论邓克尔算子正交斯特里查兹估计中的沙腾指数

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2024-10-06 DOI:10.1007/s13324-024-00970-7

Sunit Ghosh, Jitendriya Swain

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引用次数: 0

摘要

Senapati 等人（J Geom Anal 34:74, 2024）以及 Mondal 和 Song（Israel J Math, 2023）推导了与 Dunkl 拉普拉奇和 Dunkl-Hermite 算子相关的薛定谔方程的正交 Strichartz 估计。在本文中，我们构建了一组 Dunkl 设置中的相干态，并应用半经典分析推导出了上述正交 Strichartz 估计的 Schatten 指数的必要条件，结果证明该条件对于与拉普拉斯和赫尔米特算子相关的薛定谔方程是最优的。

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On the Schatten exponent in orthonormal Strichartz estimate for the Dunkl operators

The orthonormal Strichartz estimates for the Schrödinger equation associated to the Dunkl Laplacian and the Dunkl-Hermite operator are derived in Senapati et al. (J Geom Anal 34:74, 2024) and Mondal and Song (Israel J Math, 2023). In this article we construct a set of coherent states in the Dunkl setting and apply semi-classical analysis to derive a necessary condition on the Schatten exponent for the aforementioned orthonormal Strichartz estimates, which turns out to be optimal for the Schrödinger equations associated with Laplacian and Hermite operator as a particular case.

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来源期刊

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.