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arXiv · 2403.07253

Bourgain's counterexample in the sequential convergence problem for the Schr\"odinger equation

Chu-Hee Cho·Daniel Eceizabarrena
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Abstract

We study the problem of pointwise convegence for the Schr\"odinger operator on $\mathbb R^n$ along time sequences. We show that the sharp counterexample to the sequential Schr\"odinger maximal estimate given recently by Li, Wang and Yan based in the construction by Luc\`a and Rogers can also be achieved with the construction of Bourgain, and we extend it to the fractal setting.

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Chu-Hee Cho, Daniel Eceizabarrena. 2024-03-12. Bourgain's counterexample in the sequential convergence problem for the Schr\"odinger equation. https://doi.org/10.1007/s00041-025-10162-x

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