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Formal power series and Hadamard product. (Séries formelles et produit de Hadamard.) (French) Zbl 0898.11006

The main part of this paper is devoted to the presentation of the theory of formal power series which is related to the Hadamard product. The author is interested in the case of several variables, for which – in constrast to the one variable case – very little is known; for example the problems of Hadamard quotients and of the determination of units, zeros, divisors, …are still open. Many instructive examples show the difficulty of these problems. The paper ends with several new results on the Hadamard quotient problem in the several variable case.

MSC:

11B99 Sequences and sets
13J05 Power series rings
11B37 Recurrences
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References:

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