Talks given at NuHAG events

Nazarov's uncertainty principle in higher dimension

  Philippe Jaming

  given at  strobl07 (20.06.07 09:30)
  id:  639
  length:  25min
  status:  accepted
  type:  talk
In this talk we prove that there exists a constant $C$ such that, if $S,\Sigma$ are subsets of $\R^d$ of finite measure, then for every function $f\in L^2(\R^d)$,
$$\int_{\R^d}|f(x)|^2 dx \leq C e^{C \min(|S||\Sigma|, |S|^{1/d}w(\Sigma), w(S)|\Sigma|^{1/d})} (\int_{\R^d\setminus S}|f(x)|^2 dx + \int_{\R^d\setminus\Sigma}|\hat{f}(x)|^2 dx) $$
where $\hat{f}$ is the Fourier transform of $f$ and $w(\Sigma)$ is the mean width of $\Sigma$. This extends to dimension $d\geq 1$ a result of Nazarov in dimension $d=1$.

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