A1 Journal article (refereed)
On the Landis conjecture for the fractional Schrödinger equation (2023)
Kow, P.-Z. (2023). On the Landis conjecture for the fractional Schrödinger equation. Journal of Spectral Theory, 12(3), 1023-1077. https://doi.org/10.4171/jst/433
JYU authors or editors
Publication details
All authors or editors: Kow, Pu-Zhao
Journal or series: Journal of Spectral Theory
ISSN: 1664-039X
eISSN: 1664-0403
Publication year: 2023
Publication date: 21/04/2023
Volume: 12
Issue number: 3
Pages range: 1023-1077
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Publication country: Germany
Publication language: English
DOI: https://doi.org/10.4171/jst/433
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/86580
Abstract
In this paper, we study a Landis-type conjecture for the general fractional Schrödinger equation ((−P)s+q)u=0. As a byproduct, we also prove the additivity and boundedness of the linear operator (−P)s for non-smooth coefficents. For differentiable potentials q, if a solution decays at a rate exp (−∣x∣1+), then the solution vanishes identically. For non-differentiable potentials q, if a solution decays at a rate exp (−∣x∣4s−14s+), then the solution must again be trivial. The proof relies on delicate Carleman estimates. This study is an extension of the work by Rüland and Wang (2019).
Free keywords: Landis conjecture; unique continuation at infinity; fractional Schrödinger equation
Contributing organizations
Ministry reporting: Yes
VIRTA submission year: 2023
JUFO rating: 1