Equivalence of differential operators in spaces of analytic functions over the Tate field (Q2730509)
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scientific article; zbMATH DE number 1631380
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivalence of differential operators in spaces of analytic functions over the Tate field |
scientific article; zbMATH DE number 1631380 |
Statements
8 August 2001
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Tate field
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space of analytic functions
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equivalent operators
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differential operators
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Equivalence of differential operators in spaces of analytic functions over the Tate field (English)
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The author studies differential operators on the space \(A_{p,R}\) of analytic functions on the disk \(\{ z\in \mathbb C_p:\;|z|_p<R\}\) in the completion \(\mathbb C_p\) of the algebraic closure of the field of \(p\)-adic numbers. NEWLINENEWLINENEWLINEAn analog of Khaplanov's theorem on the matrix representation is proved for such operators. Necessary and sufficient conditions for equivalence of two differential operators are obtained. A similar problem for operators over \(\mathbb C\) was considered by \textit{N. I. Nagnibida} [Sib. Math. J. 10, 1056-1058 (1969; Zbl 0198.42705) ].
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