The Fourier dimension is not finitely stable. (English) Zbl 1385.42003

Summary: The Fourier dimension is not, in general, stable under finite unions of sets. Moreover, the stability of the Fourier dimension on particular pairs of sets is independent from the stability of the compact Fourier dimension.


42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
28A80 Fractals
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