## Illinois Journal of Mathematics

### The rate of convergence on Schrödinger operator

#### Abstract

Recently, Du, Guth and Li showed that the Schrödinger operator $e^{it\Delta }$ satisfies $\lim_{t\rightarrow 0}e^{it\Delta }f=f$ almost everywhere for all $f\in H^{s}(\mathbb{R}^{2})$, provided that $s>1/3$. In this paper, we discuss the rate of convergence on $e^{it\Delta }(f)$ by assuming more regularity on $f$. At $n=2$, our result can be viewed as an application of the Du–Guth–Li theorem. We also address the same issue on the cases $n=1$ and $n>2$.

#### Article information

Source
Illinois J. Math., Volume 62, Number 1-4 (2018), 365-380.

Dates
Revised: 5 December 2018
First available in Project Euclid: 13 March 2019

https://projecteuclid.org/euclid.ijm/1552442667

Digital Object Identifier
doi:10.1215/ijm/1552442667

Mathematical Reviews number (MathSciNet)
MR3922421

Zentralblatt MATH identifier
07036791

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory

#### Citation

Cao, Zhenbin; Fan, Dashan; Wang, Meng. The rate of convergence on Schrödinger operator. Illinois J. Math. 62 (2018), no. 1-4, 365--380. doi:10.1215/ijm/1552442667. https://projecteuclid.org/euclid.ijm/1552442667

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