Infinite-Order Differential Operators in the Module of Formal Generalized Functions and in a Ring of Formal Power Series

被引:2
|
作者
Hefter, S. L. [1 ]
Piven, O. L. [1 ]
机构
[1] V Karazin Kharkiv Natl Univ, Kharkiv, Ukraine
关键词
D O I
10.1007/s11253-022-02116-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We obtain the general form of continuous linear mappings acting in the module of formal generalized functions over a commutative ring and commuting with the operator of differentiation (or shift). We also prove that a continuous linear mapping acting in the ring of formal power series over the valuation ring of a complete non-Archimedean field and commuting with the operator of differentiation is a differential operator of infinite order.
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页码:896 / 915
页数:20
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