Dispersive estimates for fractional order Schrödinger operators
Abstract
We prove dispersive bounds for fractional Schrödinger operators on R n \mathbb R^n of the form H = ( − Δ ) α + V H=(-\Delta )^{\alpha }+V with V V a real-valued, decaying potential and α ∉ N \alpha \notin \mathbb N . We derive pointwise bounds on the resolvent operators for all 0 > α > n 2 0>\alpha >\frac {n}{2} , a quantitative limiting absorption principle for 1 2 > α > n 2 \frac 12>\alpha >\frac {n}{2} , and establish global dispersive estimates in dimension n ≥ 2 n\geq 2 for the range n + 1 4 ≤ α > n 2 \frac {n+1}{4}\leq \alpha >\frac {n}2 .
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Differential Equations and Boundary Problems
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Communications of the American Mathematical Society
- Volume
- 6
- Issue
- 22
- Pages
- 1260–1289
- Publication date
- 22 September 2026
- Language
- EN