Logarithmic terms in asymptotic expansions of heat operator traces
Logarithmic terms in asymptotic expansions of heat operator traces
复制标题
热算子迹线渐近展开中的对数项
DOI：
10.1080/03605309808821365
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发表时间：
1998
影响因子：
1.9
通讯作者：
G. Grubb
中科院分区：
文献类型：
--
作者：
P. Gilkey;G. Grubb
设P是紧致m维无界流形上d阶椭圆型自伴正古典伪微分算子。P的热迹在中有渐近展开式，且对l= 0，1，2，.并且k= 1，2，.我们表明，在这个扩展中的所有条款的系数是非平凡的一个密集的P集。我们表明，该条款的系数是不是本地可计算的，当是一个正整数;的ramaining系数是已知的本地可计算的。- 设PB是紧致n维流形上的Dirac型算子，其边界光滑，使得结构在边界附近是乘积;这里施加谱边界条件。设n为偶数，则方程的热迹在k= 0，1，2，…中有渐近展开式;如果n是奇数，则存在没有这些项的展开式。我们表明，所有的系数（所有，但一个，如果n是奇数）是非平凡的一个密集的运营商。
Let P be an elliptic selfadjoint positive classical pseudodifferential operator of order d on a compact m-dimensional manifold without boundary. The heat trace of P has an asymptotic expansion in and tk log t for l=0,1,2,... and k=1,2,... We show that the coefficients of all terms in this expansion are non-trivial for a dense set of P. We show that the coefficient of the term is not locally computable when is a positive integer; the ramaining coefficients are known to be locally computable. —Let PB be an operator of Dirac type on a compact n-dimentional commanifold with smooth boundary such that the structures are product near the boundary; here a spectral boundary condition is imposed. Let If n is even, the heat trace of has and asymptotic expansion in and k=0,1,2,...; if n is odd, there is an expansion without the terms. We show that all coefficients (all but one if n is odd) are nontrivial for a dense set of operators.