流形上椭圆算子的相对谱不变量
Relative Spectral Invariants of Elliptic Operators on Manifolds
摘要：
引入并研究了无边界紧致光滑流形上{\it two} Laplace型和Dirac型椭圆偏微分算子的{ \it new}相对谱不变量，这些相对谱不变量既依赖于算子的本征值又依赖于算子的本征截面，包含了更多的几何信息.我们证明了存在的齐次短时间渐近的新的不变量的渐近展开的系数是积分的一些不变量，取决于这两个运营商的符号。前两个系数的渐近展开计算明确。
英文摘要：
We introduce and study {\it new} relative spectral invariants of {\it two} elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depend on both the eigenvalues and the eigensections of these operators and contain much more information about geometry. We prove the existence of the homogeneous short time asymptotics of the new invariants with the coefficients of the asymptotic expansion being integrals of some invariants that depend on the symbols of both operators. The first two coefficients of the asymptotic expansion are computed explicitly.
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