Sharp embeddings between weighted Paley-Wiener spaces

Autor:	Carneiro, Emanuel, González-Riquelme, Cristian, Oliveira, Lucas, Olivo, Andrea, Ombrosi, Sheldy, Ramos, Antonio Pedro, Sousa, Mateus
Rok vydání:	2023
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Analysis of PDEs 46E22 42A05 42B35 30H45 33C10
Druh dokumentu:	Working Paper
Popis:	In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By means of radial symmetrization mechanisms, we show that such problems can all be shifted to dimension one. We provide precise asymptotics in the general case and, in some particular situations, we are able to identify the sharp constants and characterize the extremizers. The sharp constant study is actually a consequence of a more general result we prove in the setup of de Branges spaces of entire functions, addressing the operator given by multiplication by $z^k$, $k \in \mathbb{N}$. Applications to sharp higher order Poincar\'{e} inequalities and other related extremal problems are discussed. Comment: 43 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.06442 Zobrazit plný text záznamu View this record from Arxiv