多维超度量伪微分方程
Multidimensional ultrametric pseudodifferential equations
摘要：
本文研究了定义为局部紧超度量空间乘积的多维超度量空间上的小波和伪微分算子。在多维超度量空间上引入了小波基、广义函数空间和Lizorkin广义函数。我们还考虑了多维超度量空间上的一类伪微分算子。引入超度量拟微分方程Cauchy问题和超度量特征的概念。证明了柯西问题解的存在唯一性定理（类似于Kovalevskaya定理）。
英文摘要：
We develop an analysis of wavelets and pseudodifferential operators on multidimensional ultrametric spaces which are defined as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions and Lizorkin generalized functions on multidimensional ultrametric spaces. We also consider some family of pseudodifferential operators on multidimensional ultrametric spaces. The notions of Cauchy problem for ultrametric pseudodifferential equations and of ultrametric characteristics are introduced. A theorem about existence and uniqueness of the solution for the Cauchy problem (the analogue of the Kovalevskaya theorem) is proven.
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