The fractal uncertainty principle via Dolgopyat's method in higher dimensions
We prove a fractal uncertainty principle with exponent \(\frac{d}{2} - \delta + \varepsilon\), \(\varepsilon > 0\), for Ahlfors--David regular subsets of \(\mathbb R^d\) with dimension \(\delta\) which satisfy a suitable "nonorthogonality condition". This generalizes the application of...
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description | We prove a fractal uncertainty principle with exponent \(\frac{d}{2} - \delta + \varepsilon\), \(\varepsilon > 0\), for Ahlfors--David regular subsets of \(\mathbb R^d\) with dimension \(\delta\) which satisfy a suitable "nonorthogonality condition". This generalizes the application of Dolgopyat's method by Dyatlov--Jin (arXiv:1702.03619) to prove the same result in the special case \(d = 1\). As a corollary, we get a quantitative spectral gap for the Laplacian on convex cocompact hyperbolic manifolds of arbitrary dimension with Zariski dense fundamental groups. |
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This generalizes the application of Dolgopyat's method by Dyatlov--Jin (arXiv:1702.03619) to prove the same result in the special case \(d = 1\). As a corollary, we get a quantitative spectral gap for the Laplacian on convex cocompact hyperbolic manifolds of arbitrary dimension with Zariski dense fundamental groups.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Fractals ; Principles ; Uncertainty principles</subject><ispartof>arXiv.org, 2023-10</ispartof><rights>2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). 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title | The fractal uncertainty principle via Dolgopyat's method in higher dimensions |
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