Time decay of scaling critical electromagnetic Schrödinger flows

Abstract

We obtain a representation formula for solutions to Schrödinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the sharp $L^1\to L^{\infty }$ time decay estimate for the 3D-inverse square and the 2D-Aharonov-Bohm potentials.

32 pages, 1 figure

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• Dispersive estimates for Schrodinger operators in dimensions one and three
• The $L^p$ boundedness of wave operators for Schrödinger operators with threshold singularities II. Even dimensional case
• A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions
• Endpoint Strichartz estimates for the magnetic Schrodinger equation

Cited by in corpus (1)

• The forward problem for the electromagnetic Helmholtz equation with critical singularities