Dispersive estimates of fourth order Schr\"odinger operators with scaling-critical magnetic potentials in dimension two

TL;DR

This paper establishes dispersive estimates for a fourth order Schrödinger operator with critical magnetic potentials in two dimensions, using resolvent kernel construction and stationary phase techniques.

Contribution

It introduces a novel approach to obtain dispersive estimates for higher-order Schrödinger operators with critical magnetic potentials in two dimensions.

Findings

Dispersive estimates are successfully derived for the operator.

The method involves resolvent kernel construction and stationary phase analysis.

Results extend understanding of magnetic effects in higher-order quantum operators.

Abstract

Dispersive estimate for the fourth order Schr\"odinger operator with a class of scaling-critical magnetic potentials in dimension two was obtained by the construction of the corresponding resolvent kernel and the stationary phase method.