A Faber-Krahn inequality for wavelet transforms
| Autor: | Ramos, João P. G., Tilli, Paolo |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For some special window functions $\psi_{\beta} \in H^2(\mathbb{C}^+),$ we prove that, over all sets $\Delta \subset \mathbb{C}^+$ of fixed hyperbolic measure $\nu(\Delta),$ the ones over which the Wavelet transform $W_{\overline{\psi_{\beta}}}$ with window $\overline{\psi_{\beta}}$ 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 D\"orfler. 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. Comment: 16 pages |
| Databáze: | arXiv |
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