Landis-type conjecture for the half-Laplacian
Abstract
In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of the fractional Schrödinger equation with drift and potential terms. We show that if any solution of the equation decays at a certain exponential rate, then it must be trivial. The main ingredients of our proof are the Caffarelli-Silvestre extension and Armitage’s Liouville-type theorem.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society (AMS)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202305112994Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0002-9939
DOI
https://doi.org/10.1090/proc/16093
Language
English
Published in
Proceedings of the American Mathematical Society
Citation
- Kow, P.-Z., & Wang, J.-N. (2023). Landis-type conjecture for the half-Laplacian. Proceedings of the American Mathematical Society, 151(7), 2951-2962. https://doi.org/10.1090/proc/16093
License
Funder(s)
Research Council of Finland
European Commission
Funding program(s)
Centre of Excellence, AoF
ERC Consolidator Grant
Huippuyksikkörahoitus, SA
ERC Consolidator Grant
Additional information about funding
The first author was partially supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, 312121) and by the European Research Council under Horizon 2020 (ERC CoG 770924). The second author was partially supported by MOST 108-2115-M-002-002-MY3 and MOST 109-2115-M-002-001-MY3.
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