Cantor uniqueness and multiplicity along subsequences

TL;DR

This paper investigates the conditions under which trigonometric series can converge to zero along subsequences, revealing the sparsity and support size constraints necessary for such convergence.

Contribution

It constructs a specific trigonometric series with zero convergence on a subsequence and establishes the sparsity and support size conditions for such series.

Findings

Series with zero convergence require sparse subsequences

Support of related distribution must be large

Constructed series with coefficients tending to zero

Abstract

We construct a trigonometric series converging to zero everywhere on a subsequence, with coefficients tending to zero. We show that any such series must satisfy that the subsequence is very sparse, and that the support of the related distribution is quite large.