论文标题
分数连接拉普拉斯人的逆问题
An inverse problem for fractional connection Laplacians
论文作者
论文摘要
考虑一个分数运算符$ p^s $，$ 0 <s <1 $，用于连接laplacian $ p：= \ nabla^*\ nabla+a $ a $在平稳的Hermitian矢量捆绑包上，上面有一个封闭的，连接的，连接的Riemannian Dimension $ n \ egeq 2 $。我们表明，与$ p^s $相关的指标，遗产捆绑，连接，潜在和源头映射的本地知识在全球范围内决定了这些结构。这扩展了针对分数Laplace-Beltrami操作员已知的结果。
Consider a fractional operator $P^s$, $0<s<1$, for connection Laplacian $P:=\nabla^*\nabla+A$ on a smooth Hermitian vector bundle over a closed, connected Riemannian manifold of dimension $n\geq 2$. We show that local knowledge of the metric, Hermitian bundle, connection, potential, and source-to-solution map associated with $P^s$ determines these structures globally. This extends a result known for the fractional Laplace-Beltrami operator.
