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arXiv · 2311.11025

Estimation of function's supports under arithmetic constraints

Norbert Hegyvári
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Abstract

The well-known $|supp(f)||supp(\widehat{f}|\geq |G|$ inequality gives lower estimation of each supports. In the present paper we give upper estimation under arithmetic constrains. The main notion will be the additive energy which plays a central role in additive combinatorics. We prove an uncertainty inequality that shows a trade-off between the total changes of the indicator function of a subset $A\subseteq \mathbb F^n_2$ and the additive energy of $A$ and the Fourier spectrum.

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Norbert Hegyvári. 2023-11-18. Estimation of function's supports under arithmetic constraints. https://arxiv.org/abs/2311.11025

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