论文标题
小波变换的Faber-Krahn不平等
A Faber-Krahn inequality for wavelet transforms
论文作者
论文摘要
对于某些特殊的窗口函数，$ n^2（\ Mathbb {c}^+）中的$ψ_β\，$我们证明，所有设置$δ\ subset \ subset \ subset \ mathbb {c}^+$的固定双曲线度量$ n $ wavelet transform $ w _ phund whind pline $ w _ { $ \ OVILLINE {ψ_β} $浓缩物恰恰是相对于上半部空间的伪液压指标的盘。这回答了Abreu和Dörfler提出的一个问题。 我们的技术利用了F. Nicola和第二作者的先前作品中最近开发的框架，但在小波变换的扩张对称性引起的双曲线环境中。在我们的分析中，这自然会导致我们使用双曲线重排函数以及双曲线等数不平等。
For some special window functions $ψ_β \in H^2(\mathbb{C}^+),$ we prove that, over all sets $Δ\subset \mathbb{C}^+$ of fixed hyperbolic measure $ν(Δ),$ the ones over which the Wavelet transform $W_{\overline{ψ_β}}$ with window $\overline{ψ_β}$ concentrates optimally are exactly the discs with respect to the pseudohyperbolic metric of the upper half space. This answers a question raised by Abreu and Dörfler. Our techniques make use of a framework recently developed in a previous work by F. Nicola and the second author, but in the hyperbolic context induced by the dilation symmetry of the Wavelet transform. This leads us naturally to use a hyperbolic rearrangement function, as well as the hyperbolic isoperimetric inequality, in our analysis.
