论文标题
决定因素和Plemelj-Smithies公式
Determinants and Plemelj-Smithies formulas
论文作者
论文摘要
我们为操作员不同代数中的决定因素建立了Plemelj-Smithies公式。特别是，我们为圆环$ \ tn $上的操作员定义了庞加莱类型的决定因素，并根据符号来推导定期伪差异操作员的决定因素的公式。另一方面，通过应用最近引入的不变算子相对于希尔伯特空间的固定分解的概念，我们还获得了针对痕量类别的决定因素的公式。该分析利用了完整矩阵符号的相应概念。我们还为与紧凑的谎言基团以及在紧凑的均匀歧管上相关的椭圆算子，紧凑的谎言组以及均质矢量束上的决定因素提供了明确的公式。
We establish Plemelj-Smithies formulas for determinants in different algebras of operators. In particular we define a Poincaré type determinant for operators on the torus $\Tn$ and deduce formulas for determinants of periodic pseudo-differential operators in terms of the symbol. On the other hand, by applying a recently introduced notion of invariant operators relative to fixed decompositions of Hilbert spaces we also obtain formulae for determinants with respect to the trace class. The analysis makes use of the corresponding notion of full matrix-symbol. We also derive explicit formulas for determinants associated to elliptic operators on compact manifolds, compact Lie groups, and on homogeneous vector bundles over compact homogeneous manifolds.
