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Generalized Powers of Substitution with Pre-Function Operators

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An operator on formal power series of the form *S* *μS* , where *μ* is an invertible power series, and σ is a series of the form t+（t^{2}） is called a unipotent substitution with pre-function. Such operators, denoted by a pair (*μ *，σ ） , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .

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*Applied Mathematics*, Vol. 4 No. 7A, 2013, pp. 12-17. doi: 10.4236/am.2013.47A004.

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