On the Landis conjecture for the fractional Schrödinger equation
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).
Main Author
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
European Mathematical Society - EMS - Publishing House GmbH
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202304252691Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1664-039X
DOI
https://doi.org/10.4171/jst/433
Language
English
Published in
Journal of Spectral Theory
Citation
- 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
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Additional information about funding
This research is partially supported by MOST 105-2115-M-002-014-MY3, MOST 108-2115-M-002-002-MY3, and MOST 109-2115.
Copyright© 2023 European Mathematical Society. Published by EMS Press.