p-adic域上一类拟微分方程的定解问题
Explicit solutions to a class of pseudodifferential equations over p-adic field
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摘要: 利用p-adic域上定义的拟微分算子以及L2空间上的一组正交基,研究了p-adic域上一类拟微分方程,得到该微分方程的形式解,以及解在函数类中的收敛性质.并举例做了相关验证.Abstract: Explicit solutions to a class of pseudodifferential equations over p-adic field Kp was investigated where T is a p-adic psedodifferential operator defined by SU Weiyi.The explicit solution of the equation was obtained,and the uniqueness of solution which belongs to mixed classes of real and p-adic functions was constructed.Finally,some examples were given.