Dispersive and Strichartz Estimates for Schrödinger Equation with One Aharonov–Bohm Solenoid in a Uniform Magnetic Field

We obtain dispersive and Strichartz estimates for solutions to the Schrödinger equation with one Aharonov–Bohm solenoid in the uniform magnetic field. The main step of the proof is the construction of the Schrödinger kernel, and the main obstacle is to obtain the explicit representation of the kernel, which requires a large set of careful calculations. To overcome this obstacle, we plan to construct the Schrödinger kernel by two different strategies. The first one is to use the Poisson summation formula as Fanelli et al. (Adv Math 400:108333, 2022), while the second one relies on the Schulman–Sunada formula in Št’ovíček (Ann Phys 376:254–282, 2017), which reveals the intrinsic connections of the heat kernels on manifolds with group actions.