论文标题
具有标量潜力的哈密顿量的光谱乘数和波传播
Spectral multipliers and wave propagation for Hamiltonians with a scalar potential
论文作者
论文摘要
我们将$ \ Mathbb r^3 $的免费Laplacian的光谱乘数扩展到了形式的$-Δ+V $的扰动汉密尔顿人的情况，其中$ v $是标量真实的潜力。 在本文中，我们证明了分解估计值，这是一种针对扰动的波传播器，mihlin乘数和分数整合界限的分散性估计，以及在最佳或几乎最佳的缩放缩放量表下，在电势和频谱多比尔本身上，波动方程式strichartz估算的全范围。
We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on $\mathbb R^3$ to the case of perturbed Hamiltonians of the form $-Δ+V$, where $V$ is a scalar real-valued potential. In this paper, we prove resolvent estimates, a dispersive bound for the perturbed wave propagator, Mihlin multiplier and fractional integration bounds, and the full range of wave equation Strichartz estimates, under optimal or almost optimal scaling-invariant conditions on the potential and on the spectral multipliers themselves.
