The L^p-continuity of wave operators for fractional order Schrödinger operators

2025/09/22 by M. Burak Erdogan, M. Burak Erdoğan, Michael Goldberg +6 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Bounded function #Fourier integral operator #Microlocal analysis #Numerical methods in engineering #Numerical methods in inverse problems #Operator theory #Order (exchange) #Spectral theorem #math.AP

paper · pdf · doi:10.48550/arxiv.2509.18003

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider fractional Schrödinger operators H=(-Δ)^α+V(x) in n dimensions with real-valued potential V when n>2α, α>1. We show that the wave operators extend to bounded operators on L^p(\mathbb Rⁿ) for all 1≤ p≤∞ under conditions on the potential that depend on n and α analogously to the case when α∈ \mathbb N. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schrödinger operator.

Citations

• L^p boundedness of wave operators for higher order schrödinger operators with threshold eigenvalues
• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
• Some physical applications of fractional Schrödinger equation
• Generalized Strichartz Inequalities for the Wave Equation

Cited by

• Dispersive estimates for fractional order Schrödinger operators

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