具有边界流形上的伪微分算子
Pseudodifferential operators on manifolds with fibred boundaries
摘要：
设$X$是一个带边带边流形.假设边界被定义为$ϕ:\pa X\longrightarrow Y,$，并令$x\in\CI(X)$为边界定义函数。该数据确定了“尖点”向量场的空间，由满足$Vx=O(x^2)$的$X$上的那些向量场$V$组成，并且它们与$ϕ;$的纤维相切，它是李代数和$\CI(X)$模块。这个李代数量化的“小演算”的伪微分算子$\PsiF*(X).$映射性质，包括有界性，正则性，Fredholm条件和符号映射讨论了这种演算。的拉普拉斯算子的光谱的“精确的cusred尖点”度量进行分析，因为是波前集相关的演算。
英文摘要：
Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $ϕ:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of those vector fields $V$ on $X$ satisfying $Vx=O(x^2)$ and which are tangent to the fibres of $ϕ;$ it is a Lie algebra and $\CI(X)$ module. This Lie algebra is quantized to the `small calculus' of pseudodifferential operators $\PsiF*(X).$ Mapping properties including boundedness, regularity, Fredholm condition and symbolic maps are discussed for this calculus. The spectrum of the Laplacian of an `exact fibred cusp' metric is analyzed as is the wavefront set associated to the calculus.
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