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A note on some variations of the maximal inequality for the fractional Schrödinger equation

2022/12/23 by Chu-hee Cho, Cho, Chu-hee, Shobu Shiraki +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2212.12373

openalex publication_date 2022/12/23 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

The purpose of this note is to provide a summary of the recent work of the authors on two variations of the pointwise convergence problem for the solutions to the fractional Schrödinger equations; convergence along a tangential line and along a set of lines, as exhibiting some new results in each setting. For the former case, we make a simple observation on a path along a tangential curve of exponential order. We discuss counterexamples for the latter case that show some of the known smooth regularities are essentially optimal.

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