A. Cohen

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math.CA2024

Fractal uncertainty in higher dimensions

Alex Cohen

We prove that if a fractal set in $R^{d}$ avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main in…

math.CA2024

Fractal uncertainty for discrete 2D Cantor sets

Alex Cohen

We prove that a self-similar Cantor set in $Z_{N} \times Z_{N}$ has a fractal uncertainty principle if and only if it does not contain a pair of orthogonal lines. The…