On a compact manitold with boundary, consider the realizations of an elliptic, possibly pseudodif-ferenlial, boundaiy value problem having a spectral cut (aiay free of eigenvalues), say R_ In the first part of the paper we define and discuss in detail the operator log B its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, f (B. 0), and it enters in an important way in studies of composed zeta functions t, (A. B s) - Tr(AS~v) (pursued elsewhere).
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机译：在带边界的紧凑型马尼托理马座上，考虑具有频谱削减（无特征值）的椭圆形，可能为伪二乘的，有边值问题的实现，例如R_。在本文的第一部分中，我们定义并详细讨论了算子log B 的残差（泛化Wodzicki残差）与零时的zeta函数值f（B. 0）基本成正比，并且它以重要方式进入组成zeta函数t（A. B s）的研究中-Tr（AS〜v）（在其他地方购买）。
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