2019/03/06 by Shobu Shiraki, Shiraki, Shobu
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 #math.AP #math.CA
paper · pdf · doi:10.48550/arxiv.1903.02356
arxiv created 2019/03/06 · openalex publication_date 2019/03/06 · arxiv updated 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the pointwise convergence problem for the solution of Schrödinger-type equations along directions determined by a given compact subset of the real line. This problem contains Carleson's problem as the most simple case and was studied in general by Cho--Lee--Vargas. We extend their result from the case of the classical Schrödinger equation to a class of equations which includes the fractional Schrödinger equations. To achieve this, we significantly simplify their proof by completely avoiding a time localization argument.