超度量空间上的伪微分算子与超度量小波
Pseudodifferential operators on ultrametric spaces and ultrametric wavelets
摘要：
在二次可积复值函数空间中引入了一类标准正交基，即超距离小波基。引入了一类作用于这些超距离空间上的复值函数的伪微分算子族。我们证明了这些算子在引入的超度量小波基中是对角的，并计算了相应的特征值。引入变量的超度量变换，将超度量空间映射到正半直线上，并利用该映射构造小波基的非齐次推广。
英文摘要：
A family of orthonormal bases, the ultrametric wavelet bases, is introduced in quadratically integrable complex valued functions spaces for a wide family of ultrametric spaces. A general family of pseudodifferential operators, acting on complex valued functions on these ultrametric spaces is introduced. We show that these operators are diagonal in the introduced ultrametric wavelet bases, and compute the corresponding eigenvalues. We introduce the ultrametric change of variable, which maps the ultrametric spaces under consideration onto positive half-line, and use this map to construct non-homogeneous generalizations of wavelet bases.
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