Dispersive estimates for fractional order Schrödinger operators

2025/09/22 by M. Burak Erdogan, M. Burak Erdoğan, Michael Goldberg +6
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #Dimension (graph theory) #Limiting #Operator (biology) #Order (exchange) #Pointwise #Range (aeronautics) #Resolvent #math.AP

paper · pdf · doi:10.48550/arxiv.2509.18002

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove dispersive bounds for fractional Schrödinger operators on \mathbb Rⁿ of the form H=(-Δ)^α+V with V a real-valued, decaying potential and α∉\mathbb N. We derive pointwise bounds on the resolvent operators for all 0<α<(n)/(2), a quantitative limiting absorption principle for \frac12<α<(n)/(2), and establish global dispersive estimates in dimension n≥ 2 for the range (n+1)/(4)≤ α<\fracn2.

Citations

• The L^p-continuity of wave operators for fractional order Schrödinger operators
• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials
• Generalized Strichartz Inequalities for the Wave Equation
• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)

Related

• The L^p-continuity of wave operators for fractional order Schrödinger operators
• Dispersive estimates for time and space fractional Schrödinger equations
• Dispersive estimates for Schroedinger operators: A survey
• Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials
• Dispersive estimates of solutions to the Schrodinger equation in dimensions n≥ 4