O. Kovrizhkin

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math.CA2002

The Uncertainty Principle for certain densities

O. Kovrizhkin

We prove a new version of the Uncertainty Principle of the form $\int ∣ f ∣^{2} ≲ \int_{E^{c}} ∣ f ∣^{2} + \int_{Σ^{c}} ∣ f^∣^{2}$ where the sets $E$ and $Σ$ are $ε$ -thin in the follow…

math.CA2002

Estimates of functions with vanishing periodizations

O. Kovrizhkin

We prove that if a function $f \in L^{p} (R^{d})$ has vanishing periodizations then $∥ f ∥_{p^{'}} ≲ ∥ f ∥_{p}$ , provided $1 \leq p < \frac{2 d}{d + 2}$ and dimension $d \g…

math.CA2000

Some results related to the Logvinenko-Sereda theorem

Oleg Kovrizhkin

We prove several results related to the theorem of Logvinenko and Sereda on determining sets for functions with Fourier transforms supported in an interval. We obtain a polynomial…