The Fourier spectrum and sumset type problems
Date
05/04/2024Author
Grant ID
EP/R015104/1
RPG-2019-034
N/A
Keywords
Metadata
Show full item recordAbstract
We 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.
Citation
Fraser , J 2024 , ' The Fourier spectrum and sumset type problems ' , Mathematische Annalen . https://doi.org/10.1007/s00208-024-02843-7
Publication
Mathematische Annalen
Status
Peer reviewed
ISSN
0025-5831Type
Journal article
Description
Funding: EPSRC Standard Grant (EP/R015104/1), a Leverhulme Trust Research Project Grant (RPG-2019-034) and an RSE Sabbatical Research Grant (70249).Collections
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