TL;DR
This paper extends Wik's theorem to show the existence of massive Helson sets with Hausdorff dimension one in multidimensional settings, broadening the understanding of these sets beyond the circle.
Contribution
The paper generalizes Wik's result from the circle to higher-dimensional spaces, demonstrating the existence of massive Helson sets with full Hausdorff dimension.
Findings
Existence of massive Helson sets in multidimensional spaces.
Helson sets can have Hausdorff dimension one in higher dimensions.
Extension of Wik's theorem to multiple dimensions.
Abstract
According to the Wik theorem, there exist massive Helson sets on the circle. In particular, they can be of Hausdorff dimension one. We extend Wik's result to the multidimensional case.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Numerical Analysis Techniques · Mathematical Analysis and Transform Methods