# Difference between revisions of "Regressive functions form an abelian group under circle plus"

From timescalewiki

Line 1: | Line 1: | ||

==Theorem== | ==Theorem== | ||

− | Let $\mathbb{T}$ be a [[time scale]]. The structure $(\mathcal{R}(\mathbb{T},\mathbb{C}),\oplus_h)$ is an Abelian group, where $\mathcal{R}(\mathbb{T},\mathbb{ | + | Let $\mathbb{T}$ be a [[time scale]]. The structure $(\mathcal{R}(\mathbb{T},\mathbb{C}),\oplus_h)$ is an Abelian group, where $\mathcal{R}(\mathbb{T},\mathbb{C})$ denotes the set of [[forward regressive|regressive]] functions and $\oplus_h$ denotes the [[circle plus]]. |

==Proof== | ==Proof== |

## Revision as of 23:09, 14 July 2016

## Theorem

Let $\mathbb{T}$ be a time scale. The structure $(\mathcal{R}(\mathbb{T},\mathbb{C}),\oplus_h)$ is an Abelian group, where $\mathcal{R}(\mathbb{T},\mathbb{C})$ denotes the set of regressive functions and $\oplus_h$ denotes the circle plus.