Abstract
AbstractWe introduce and study the Fourier spectrum which is a continuously parametrised family of dimensions living between the Fourier dimension and the Hausdorff dimension for both sets and measures. We establish some fundamental theory and motivate the concept via several applications, especially to sumset type problems. For example, we study dimensions of convolutions and sumsets, and solve the distance set problem for sets satisfying certain Fourier analytic conditions.
Funder
Engineering and Physical Sciences Research Council
Leverhulme Trust
Royal Society of Edinburgh
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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