Sharp pointwise convergence of Schrödinger mean with complex time in higher dimensions

2025/12/26 by Meng Wang, Zhichao Wang, Wang, Meng +1
Mathematics · #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.2512.22037

Abstract

In this paper, we establish the almost everywhere convergence of solutions to the Schrödinger operator with complex time P_γf(x,t) in higher dimensions, under the assumption that the initial data f belongs to the Sobolev space H^s(ℝ^d).

Citations

• On the rate of convergence for Landau type Schrödinger Operators
• On Bourgain's counterexample for the Schrödinger maximal function
• A note on pointwise convergence for the Schrödinger equation
• On the Schrodinger maximal function in higher dimension

Related

• Sharp pointwise convergence of Schrödinger operator with complex time along curves
• Schrödinger means in higher dimensions
• Pointwise Convergence for sequences of Schrödinger means in ℝ²
• Convergence of a Class of Schrödinger Equations
• Pointwise convergence of solutions to Schrödinger equations