非齐次测度下的超度量拟微分算子与小波
Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
摘要：
在一般超距离空间上（在一定的拓扑限制下），引入了关于任意测度函数的二次可积空间中的超距离小波的标准正交基族.研究超距离空间上的伪微分算子。我们证明了这些算子在超度量小波基中是对角的，并计算了相应的特征值。讨论了超度量空间与有向树的对偶性。特别地，提出了一种利用有向树完备化构造超度量空间的新方法。
英文摘要：
A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable with respect to arbitrary measure functions on general (up to some topological restrictions) ultrametric space is introduced. Pseudodifferential operators (PDO) on the ultrametric space are investigated. We prove that these operators are diagonal in the introduced bases of ultrametric wavelets and compute the corresponding eigenvalues. Duality between ultrametric spaces and directed trees is discussed. In particular, a new way of construction of ultrametric spaces by completion of directed trees is proposed.
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