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 editorsKow, Pu-Zhao

Journal or seriesJournal of Spectral Theory

ISSN1664-039X

eISSN1664-0403

Publication year2023

Publication date21/04/2023

Volume12

Issue number3

Pages range1023-1077

PublisherEuropean Mathematical Society - EMS - Publishing House GmbH

Publication countryGermany

Publication languageEnglish

DOIhttps://doi.org/10.4171/jst/433

Publication open accessOpenly available

Publication channel open accessPartially 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 keywordsLandis conjecture; unique continuation at infinity; fractional Schrödinger equation


Contributing organizations


Ministry reportingYes

VIRTA submission year2023

JUFO rating1


Last updated on 2024-12-10 at 16:30