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| 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 $\ominus_{\mu}$ $$\ominus_h z = \dfrac{-z}{1+zh}.$$

Properties

Theorem

The circle minus $\ominus_h$ is the inverse operation of the circle plus operation $\oplus_h$. Moreover, $$z \ominus_h w = z \oplus_h (\ominus_h w).$$

Proof

References