Difference between revisions of "Forward circle minus"
From timescalewiki
| Line 1: | Line 1: | ||
| − | Let $\mathbb{T}$ be a [[time scale]] and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be [[forward regressive function| regressive]]. We define the (forward) circle minus operation $\ominus_{\mu}$ | + | Let $\mathbb{T}$ be a [[time scale]] and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be [[forward regressive function| (forward) regressive functions ]]. We define the (forward) circle minus operation $\ominus_{\mu}$ |
$$\ominus_h z = \dfrac{-z}{1+zh}.$$ | $$\ominus_h z = \dfrac{-z}{1+zh}.$$ | ||
=Properties= | =Properties= | ||
{{:Circle minus inverse of circle plus}} | {{:Circle minus inverse of circle plus}} | ||
Revision as of 23:28, 31 May 2016
Let $\mathbb{T}$ be a time scale and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be (forward) regressive functions . We define the (forward) circle minus operation $\ominus_{\mu}$ $$\ominus_h z = \dfrac{-z}{1+zh}.$$
Contents
Properties
Theorem
The circle minus $\ominus_h$ is the inverse operation of the circle plus operation $\oplus_h$. Moreover, $$z \ominus_h w = z \oplus_h (\ominus_h w).$$
