Difference between revisions of "Forward circle minus"
From timescalewiki
(Created page with "Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the Hilger complex plane. We define the $\ominus_h$ operation by $$\ominus_h z = \dfrac{-z}{1+zh}.$$ =Properties= <div class="to...") |
|||
| (12 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | Let $ | + | 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 by |
| − | $$\ | + | $$\left( \ominus_{\mu} p \right)(t) = \dfrac{-p(t)}{1+p(t)\mu(t)}.$$ |
| + | Often in the literature, the subscript is suppressed. | ||
=Properties= | =Properties= | ||
| − | < | + | [[Forward regressive functions form a group]]<br /> |
| − | + | [[Circle minus inverse of circle plus]]<br /> | |
| − | + | ||
| − | + | =See Also= | |
| − | < | + | [[Delta exponential]]<br /> |
| − | + | ||
| − | + | =References= | |
| + | |||
| + | [[Category:Definition]] | ||
Latest revision as of 15:26, 21 January 2023
Let $\mathbb{T}$ be a time scale and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be (forward) regressive functions . We define the (forward) circle minus operation by $$\left( \ominus_{\mu} p \right)(t) = \dfrac{-p(t)}{1+p(t)\mu(t)}.$$ Often in the literature, the subscript is suppressed.
Properties
Forward regressive functions form a group
Circle minus inverse of circle plus
