Bourgain's counterexample in the sequential convergence problem for the Schrödinger equation

2024/03/12 by Chu-hee Cho, Cho, Chu-Hee, Daniel Eceizabarrena +1
Computer Science · Mathematics · #35J10 #42B37 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2403.07253

openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of pointwise convegence for the Schrödinger operator on \mathbb Rⁿ along time sequences. We show that the sharp counterexample to the sequential Schrödinger maximal estimate given recently by Li, Wang and Yan based in the construction by Lucà and Rogers can also be achieved with the construction of Bourgain, and we extend it to the fractal setting.

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