Heat Operator Trace Expansions and Index for General Atiyah–Patodi–Singer Boundary Problems
Heat Operator Trace Expansions and Index for General Atiyah–Patodi–Singer Boundary Problems
复制标题
一般 Atiyah-Patodi-Singer 边界问题的热算子迹展开和索引
DOI：
10.1080/03605309208820913
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发表时间：
1992
影响因子：
1.9
通讯作者：
G. Grubb
中科院分区：
文献类型：
--
作者：
G. Grubb
在基础论文[APS]中，Atiyah，Patoki和Singer给出了某些一阶椭圆微分算子P的指数公式：C[infinity]（E）[yield] C[infinity]（F），其中E和F是具有边界Y的紧致n维C[infinity]流形X上的Hermitian C[infinity]向量丛，假设该算子以及流形和丛在边界附近具有乘积结构。在本文中，我们对待一般的非产品的情况下，推导出一个公式，一个新的边界项，我们建立渐近展开的热算子与问题，没有单独处理之前。
In the fundamental paper [APS], Atiyah, Patoki and Singer showed a formula for the index of certain first order elliptic differential operators P:C[infinity](E) [yields] C[infinity](F), where E and F are Hermitian C[infinity] vector bundles over a compact n-dimensional C[infinity] manifold X with boundary Y, under the assumption that the operator as well as the manifold and bundles have a product structure near the boundary. In the present paper we treat the general non-product case, deriving a formula with a new boundary term; and we establish asymptotic expansions of the heat operators associated with the problem, that have not been treated individually before.