Infinite order differential operators in the module of formal generalized functions and in a ring of formal power series
Abstract
UDC 517.983
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 differentiation or shift operator. We also prove that a continuous linear mapping acting in the ring of formal power series over the valuation ring of a complete non-Archimedian field and commuting with the differentiation is a differential operator of infinite order.
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