Ihyeok Seo

Unique continuation for fractional Schrödinger operators in three and higher dimensions

We prove the unique continuation property for the differential inequality

Global Well-Posedness for Higher-Order Schrödinger Equations in Weighted L2 Spaces

|(-\Delta)^{\alpha/2}u|\leq|V(x)u|

From resolvent estimates to unique continuation for the Schrödinger equation

, where

CARLEMAN INEQUALITIES FOR FRACTIONAL LAPLACIANS AND UNIQUE CONTINUATION

0<\alpha<n

On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications

and

On weighted ² estimates for solutions of the wave equation

V\in L_{\textrm{loc}}^{n/\alpha,\infty}(\mathbb{R}^n)

Inhomogeneous Strichartz estimates for Schrödinger's equation

,

On a reverse H\"older inequality for Schr\"odinger operators.

n\geq3

Strichartz and smoothing estimates in weighted

.

L^2

We obtain the global well-posedness for Schrödinger equations of higher orders in weighted L2 spaces. This is based on weighted L2 Strichartz estimates for the corresponding propagator with higher-order dispersion. Our method is also applied to the Airy equation which is the linear component of Korteweg-de Vries type equations.