6533b854fe1ef96bd12af539
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On the Landis conjecture for the fractional Schrödinger equation
Pu-zhao Kowsubject
fractional Schrödinger equationLandis conjectureunique continuation at infinityStatistical and Nonlinear PhysicsGeometry and TopologyMathematical Physicsdescription
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). peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2023-04-21 | Journal of Spectral Theory |