The Dirac Equation in Two Dimensions: Dispersive Estimates and Classification of Threshold Obstructions

摘要: We investigate dispersive estimates for the two dimensional Dirac equation with a potential. In particular, we show that evolution satisfies t−1 decay rate as an operator from Hardy space H1 to BMO, of functions bounded mean oscillation. This estimate, along L2 conservation law allows one deduce family Strichartz estimates. classify structure threshold obstructions being composed s-wave resonances, p-wave resonances and eigenfunctions. that, in case Schrodinger evolution, presence resonance does not destroy rate. As consequence our analysis obtain limiting absorption principle neighborhood threshold, there are only finitely many eigenvalues spectral gap.