相干态的Sharp不等式及其优化器

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2022-10-26 DOI:10.1515/ans-2022-0050

R. Frank

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引用次数: 7

摘要

摘要我们对与Wehrl猜想及其推广有关的相干态变换的尖锐函数不等式感兴趣。这个猜想是由Lieb在海森堡群的情况下解决的，Lieb和Solovej对SU（2），Kulikov对SU（1，1）和仿射群。在本文中，我们首次给出了一般情况下的优化器的替代证明和特征。我们还将最近由Nicola和Tilli引起的海森堡相干态的Faber-Krahn型不等式推广到SU（2）和SU（1，1）的情况。最后，我们证明了Bodmann猜想的一组多项式的逆Hölder不等式。

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Sharp inequalities for coherent states and their optimizers

Abstract We are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the Heisenberg group, Lieb and Solovej for SU(2), and Kulikov for SU(1, 1) and the affine group. In this article, we give alternative proofs and characterize, for the first time, the optimizers in the general case. We also extend the recent Faber-Krahn-type inequality for Heisenberg coherent states, due to Nicola and Tilli, to the SU(2) and SU(1, 1) cases. Finally, we prove a family of reverse Hölder inequalities for polynomials, conjectured by Bodmann.

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来源期刊

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.