Generalized Powers of Substitution with Pre-Function Operators

• 作者: Laurent Poinsot
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: FORMAL Power Series FORMAL SUBSTITUTION Riordan Group GENERALIZED POWERS Sheffer Sequences Umbral CALCULUS
• 年，卷（期）: 2013,（7）
• 页码范围: 12-17
• 页数: 6页
• 分类号: O1

摘要

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 .