论文标题
差异操作员的拉普拉斯不变
Laplace invariants of differential operators
论文作者
论文摘要
我们确定有大量自然类别的偏差算子类别的条件，可以构建一组完整的拉普拉斯不变性。为此，我们研究了量规变换下部分差分运算符差异不变的一般特性，并引入了足够的条件，以使一组不变式完成。我们还提供了一些温和的条件，可以保证存在这种集合。证明是建设性的。该方法给出了许多先前在文献中已知的不变性的例子以及包括多维的许多新示例。
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential invariants of partial differential operators under gauge transformations and introduce a sufficient condition for a set of invariants to be complete. We also give a some mild conditions that guarantee the existence of such a set. The proof is constructive. The method gives many examples of invariants previously known in the literature as well as many new examples including multidimensional.
