Generalized Powers of Substitution with Pre-Function Operators

DOI: 10.4236/am.2013.47A004   PDF   HTML   XML   2,646 Downloads   4,017 Views   Citations

Abstract

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+(t2) 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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L. Poinsot, "Generalized Powers of Substitution with Pre-Function Operators," Applied Mathematics, Vol. 4 No. 7A, 2013, pp. 12-17. doi: 10.4236/am.2013.47A004.

Conflicts of Interest

The authors declare no conflicts of interest.

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