Difference between revisions of "Forward jump"
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Let $\mathbb{T}$ be a [[time scale]]. The forward jump operator $\sigma \colon \mathbb{T}^{\kappa} \rightarrow \mathbb{T}$ is defined by the formula | Let $\mathbb{T}$ be a [[time scale]]. The forward jump operator $\sigma \colon \mathbb{T}^{\kappa} \rightarrow \mathbb{T}$ is defined by the formula | ||
$$\sigma(t)=\inf \left\{ x \in \mathbb{T} \colon x > t \right\}.$$ | $$\sigma(t)=\inf \left\{ x \in \mathbb{T} \colon x > t \right\}.$$ | ||
| + | |||
| + | =Properties= | ||
| + | [[Forward jump is rd-continuous]]<br /> | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Time scale|next=Induction on time scales}}: Definition 1.1 | ||
| + | * {{PaperReference|Partial dynamic equations on time scales|2006|Billy Jackson||prev=Multiples of integers|next=Backward jump}}: Appendix | ||
| + | * {{PaperReference|Functional series on time scales|2008|Dorota Mozyrska|author2=Ewa Pawluszewicz|prev=Time scale|next=Backward jump}} | ||
Latest revision as of 14:51, 15 January 2023
Let $\mathbb{T}$ be a time scale. The forward jump operator $\sigma \colon \mathbb{T}^{\kappa} \rightarrow \mathbb{T}$ is defined by the formula $$\sigma(t)=\inf \left\{ x \in \mathbb{T} \colon x > t \right\}.$$
Properties
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Definition 1.1
- Billy Jackson: Partial dynamic equations on time scales (2006)... (previous)... (next): Appendix
- Dorota Mozyrska and Ewa Pawluszewicz: Functional series on time scales (2008)... (previous)... (next)
