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
Julkaistu sarjassa
Journal of Spectral TheoryTekijät
Päivämäärä
2023Tekijänoikeudet
© 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).
Julkaisija
European Mathematical Society - EMS - Publishing House GmbHISSN Hae Julkaisufoorumista
1664-039XJulkaisu tutkimustietojärjestelmässä
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.Lisenssi
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