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