Uniqueness of the Kontsevich-Vishik trace
Uniqueness of the Kontsevich-Vishik trace
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Kontsevich-Vishik 轨迹的独特性
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
J. Seiler
中科院分区：
文献类型：
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作者：
L. Maniccia;E. Schrohe;J. Seiler
设 M 为闭流形。我们证明 Kontsevich-Vishik 迹是在 M 上的所有经典伪微分算子的集合上定义的，其（复）阶不是大于或等于暗淡 M 的整数，是唯一的泛函，它 (i) 在其域上是线性的，(ii) 具有迹属性，并且 (iii) 与迹类算子上的 L 2 算子迹一致。此外，对奇维流形上任意整数阶的偶偶伪微分算子的扩展以及对偶维流形上任意整数阶的偶奇伪微分算子的扩展是唯一的。
Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M, whose (complex) order is not an integer greater than or equal to - dim M, is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L 2 -operator trace on trace class operators. Also the extension to even-even pseudodifferential operators of arbitrary integer order on odd-dimensional manifolds and to even-odd pseudodifferential operators of arbitrary integer order on even-dimensional manifolds is unique.