论文标题
Schrödinger操作员在平坦的欧几里得锥上的分解和光谱测量
Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones
论文作者
论文摘要
我们在平坦的Euclidean Cone $（x，g）$上构建了Resolvent的Schwartz内核和Schrödinger操作员的光谱测量，其中$ x = C（\ Mathbb {s}_σ^1）=（0，\ infty） $ \ mathbb {s}_σ^1 = \ r/2πσ\ z $，带有半径$σ> 0 $，公制$ g = dr^2+r^2dθ^2 $。作为产品，我们在这种情况下证明了Schrödinger和半波传播器的分散估计。
We construct the Schwartz kernel of resolvent and spectral measure for Schrödinger operators on the flat Euclidean cone $(X,g)$, where $X=C(\mathbb{S}_σ^1)=(0,\infty)\times \mathbb{S}_σ^1$ is a product cone over the circle, $\mathbb{S}_σ^1=\R/2πσ\Z$, with radius $σ>0$ and the metric $g=dr^2+r^2 dθ^2$. As products, we prove the dispersive estimates for the Schrödinger and half-wave propagators in this setting.
