The expansion of the resolvent near a singular stratum of conical type
The expansion of the resolvent near a singular stratum of conical type
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圆锥形奇异层附近溶解物的膨胀
DOI：
10.1016/0022-1236(91)90030-9
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发表时间：
1991
影响因子：
1.7
通讯作者：
R. Seeley
中科院分区：
文献类型：
--
作者：
J. Brüning;R. Seeley
本文将文献[BS 2]中孤立圆锥奇点的分析推广到任意维的奇异地层。它给出了tr（d+ A）-"，A-++ 03的一个展开式，对于适当大的m，以I的降幂表示.系数由与拉普拉斯算子在非奇异点相关的通常密度的积分给出，在奇异层适当正则化，加上奇异项作为奇异层上的积分给出。一个具体的例子是一个“楔形”WC M”在黎曼流形M。除了沿着由SE UP-“参数化的奇异地层C之外，W的边界是光滑的。在C附近，~ 3 W= Z，uZ，，其中C1和C2在C中横向相交。在一个垂直于Z的平面截面上，在点S处，C和Z2以一个角CL（S）> 0相交，在W内测量。在C的邻域中引入坐标（x1，x2，S），其中
This paper extends the analysis of an isolated conical singularity in [BS2] to singular strata of arbitrary dimension. It gives an expansion of tr (d+ A)-“, A-++ 03, in descending power of I, for suitably large m. The coefficients are given by integrals of the usual densities associated with the Laplacian at nonsingular points, suitably regularized at the singular stratum, plus singular terms given as integrals over the singular stratum. A concrete example of the situation treated is a “wedge” WC M” in a Riemannian manifold M. The boundary of W is smooth except along a singular stratum C parametrized by SE UP-‘. Near C,~ 3 W= Z, u Z,, with C, and C2 intersecting transversally in C. In a plane section perpendicular to Z at a point S, C, and Z2 meet at an angle CL (S)> 0, measured inside W. Introduce coordinates (x1, x2, S) in a neighborhood of C, where