arXiv subjects
Publications and source records attributed to O. Kovrizhkin.
We prove a new version of the Uncertainty Principle of the form $\int |f|^2 \lesssim \int_{E^c} |f|^2 + \int_{Σ^c}|\hat f|^2 $ where the sets $E$ and $Σ$ are $ε$-thin in the following sense: $|E \cap D(x, ρ_1(x))| \le ε|D(x, ρ_1(x))|$ and $|Σ\cap D(x, ρ_2(x))| \le ε|D(x, ρ_2(x))|$. This is an intermediate result between Logvinenko-Sereda's and Wolff's versions of the Uncertainty Principle.
We obtain a new version of the Uncertainty Principle for functions with Fourier transforms supported on a lacunary set of intervals. This is a generalization of Zygmund's theorem on lacunary trigonometric series to the real line in the spirit of the Logvinenko-Sereda theorem for relatively dense sets.
We prove that if a function $f \in L^p({\Bbb {R}} ^d)$ has vanishing periodizations then $\|f\|_{p'} \lesssim \|f\|_{p}$, provided $1 \le p < \frac {2d}{d + 2}$ and dimension $d \ge 3$.