Optimization and Control Theory Department: 2011-06-08 Seminar

Xiao-Xiong Gan
(Mathematics Department, Morgan State University, Baltimore, USA)

Composition and Generalized Composition of Formal Power Series

Given two formal power series

$f(z) = \sum_{n=1}^{\infty} a_n z^n$ and $g(z)=\sum_{n=0}^{\infty} b_n z^n$

the composition $g \circ f$ has been a very interesting topic for many years, where $f$ is called the nonunit. If $f(z) =\sum_{n=0}^{\infty} a_n z^n$ with $a_0 \neq 0$ , such a composition $g \circ f$ is called the generalized composition if it exists. We introduce the history of these two compositions and some results of them. Both of them are applied widely although the generalized composition is much younger than the regular one.

The seminar will take place at 9:00.