We establish a version of the fractal uncertainty principle, obtained by Bourgain and Dyatlov in 2016, in higher dimensions. The Fourier support is limited to sets Y ⊂ Rd which can be covered by finitely many products of δ-regular sets in one dimension, but relative to arbitrary axes. Our results remain true if Y is distorted by diffeomorphisms. Our method combines the original approach by Bourgain and Dyatlov, in the more quantitative 2017 rendition by Jin and Zhang, with Cartan set techniques
Let $f:\widehat{\mathbb{C}}\rightarrow \widehat{\mathbb{C}}$ be a hyperbolic rational map of degree ...
AbstractWe establish a higher-dimensional version of multifractal analysis for several classes of hy...
We show directly that the fractal uncertainty principle of Bourgain–Dyatlov [3] implies that there e...
We show a fractal uncertainty principle with exponent 1/2-δ+ε, ε > 0, for Ahlfors-David regular subs...
Fractal uncertainty principles (FUPs) in harmonic analysis quantify the extent to which a function a...
AbstractIn this paper we prove that there exists a constant C such that, if S,Σ are subsets of Rd of...
Motivated by results of Dyatlov on Fourier uncertainty principles for Cantor sets and by similar res...
An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbe...
AbstractIn recent years many deterministic parabolic equations have been shown to possess global att...
In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean...
We study the fractal pointwise convergence for the equation $i\hbar\partial_tu + P(D)u = 0$, where t...
AbstractWe prove estimates of the L2 norms on relatively dense subsets of the real line of functions...
I will present a new explanation of the connection between the fractal uncertainty principle (FUP) o...
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional...
Article expanding the Intrinsic Diophantine approximation on fractals first proposed by K. Mahler (1...
Let $f:\widehat{\mathbb{C}}\rightarrow \widehat{\mathbb{C}}$ be a hyperbolic rational map of degree ...
AbstractWe establish a higher-dimensional version of multifractal analysis for several classes of hy...
We show directly that the fractal uncertainty principle of Bourgain–Dyatlov [3] implies that there e...
We show a fractal uncertainty principle with exponent 1/2-δ+ε, ε > 0, for Ahlfors-David regular subs...
Fractal uncertainty principles (FUPs) in harmonic analysis quantify the extent to which a function a...
AbstractIn this paper we prove that there exists a constant C such that, if S,Σ are subsets of Rd of...
Motivated by results of Dyatlov on Fourier uncertainty principles for Cantor sets and by similar res...
An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbe...
AbstractIn recent years many deterministic parabolic equations have been shown to possess global att...
In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean...
We study the fractal pointwise convergence for the equation $i\hbar\partial_tu + P(D)u = 0$, where t...
AbstractWe prove estimates of the L2 norms on relatively dense subsets of the real line of functions...
I will present a new explanation of the connection between the fractal uncertainty principle (FUP) o...
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional...
Article expanding the Intrinsic Diophantine approximation on fractals first proposed by K. Mahler (1...
Let $f:\widehat{\mathbb{C}}\rightarrow \widehat{\mathbb{C}}$ be a hyperbolic rational map of degree ...
AbstractWe establish a higher-dimensional version of multifractal analysis for several classes of hy...
We show directly that the fractal uncertainty principle of Bourgain–Dyatlov [3] implies that there e...
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