Nazarov's uncertainty principles in higher dimension
| dc.creator | Jaming, Philippe | |
| dc.date | 2006-12-13 | |
| dc.date.accessioned | 2026-07-07T08:14:57Z | |
| dc.date.available | 2026-07-07T08:14:57Z | |
| dc.description | In this paper we prove that there exists a constant $C$ such that, if $S,Σ$ are subsets of $\R^d$ of finite measure, then for every function $f\in L^2(\R^d)$, $$\int_{\R^d}|f(x)|^2 dx \leq C e^{C \min(|S||Σ|, |S|^{1/d}w(Σ), w(S)|Σ|^{1/d})} (\int_{\R^d\setminus S}|f(x)|^2 dx + \int_{\R^d\setminusΣ}|\hat{f}(x)|^2 dx) $$ where $\hat{f}$ is the Fourier transform of $f$ and $w(Σ)$ is the mean width of $Σ$. This extends to dimension $d\geq 1$ a result of Nazarov \cite{pp.Na} in dimension $d=1$. | |
| dc.identifier | https://arxiv.org/abs/math/0612367 | |
| dc.identifier | http://arxiv.org/abs/math/0612367 | |
| dc.identifier | Journal of Approximation Theory (04/05/2007) doi:10.1016/j.jat.2007.04.005 | |
| dc.identifier | doi:10.1016/j.jat.2007.04.005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133318 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B10 | |
| dc.title | Nazarov's uncertainty principles in higher dimension | |
| dc.type | text |