Difference between revisions of "Forward circle minus"
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| − | 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 | + | 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 |
$$\left( \ominus_{\mu} p \right)(t) = \dfrac{-p(t)}{1+p(t)\mu(t)}.$$ | $$\left( \ominus_{\mu} p \right)(t) = \dfrac{-p(t)}{1+p(t)\mu(t)}.$$ | ||
| − | + | 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
