Difference between revisions of "Forward circle minus"
From timescalewiki
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=Properties= | =Properties= | ||
| − | + | [[Forward regressive functions form a group]]<br /> | |
| − | + | [[Circle minus inverse of circle plus]]<br /> | |
=See Also= | =See Also= | ||
[[Delta exponential]]<br /> | [[Delta exponential]]<br /> | ||
Revision as of 15:43, 22 September 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 $\ominus_{\mu} \colon \mathbb{T} \rightarrow \mathbb{T}$ by $$\left( \ominus_{\mu} p \right)(t) = \dfrac{-p(t)}{1+p(t)\mu(t)}.$$ Since the set of forward regressive functions form a group $\left(\mathcal{R}(\mathbb{T},\mathbb{C}),\oplus_{\mu} \right)$ under circle plus with inverse operation $\ominus_{\mu}$, we define $$p \ominus_{\mu} q = p \oplus_{\mu} (\ominus_{\mu} q).$$
Properties
Forward regressive functions form a group
Circle minus inverse of circle plus
