On the Landis conjecture for the fractional Schrödinger equation
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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Journal of Spectral TheoryAuthors
Date
2023Copyright
© 2023 European Mathematical Society. Published by EMS Press.
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).
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European Mathematical Society - EMS - Publishing House GmbHISSN Search the Publication Forum
1664-039XPublication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/182893157
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This research is partially supported by MOST 105-2115-M-002-014-MY3, MOST 108-2115-M-002-002-MY3, and MOST 109-2115.License
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