论文标题
连贯状态及其优化者的急剧不平等现象
Sharp inequalities for coherent states and their optimizers
论文作者
论文摘要
我们对与WEHRL猜想及其概括有关的连贯状态变换感兴趣。在海森伯格集团（Heisenberg Group）的情况下，Lieb解决了这一猜想，然后由Lieb and Solovej for Su（2）和Kulikov进行SU（1,1）和Aggine Group。在本文中，我们给出了替代的证据，并首次表征了一般情况下的优化器。由于尼古拉（Nicola）和蒂里（Tilli），我们还将最近对海森伯格（Heisenberg）连贯国家的Faber-Krahn型不平等扩展到SU（2）和SU（1,1）案件。最后，我们证明了由Bodmann猜想的多项式反向Hölder不平等的家族。
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 and then by Lieb and Solovej for SU(2) and by Kulikov for SU(1,1) and the affine group. In this paper, 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.
