Difference between revisions of "Forward jump"

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(Created page with "Let $\mathbb{T}$ be a time scale. The forward jump operator $\sigma \colon \mathbb{T} \rightarrow \mathbb{T}$ is defined by the formula $$\sigma(t) := \inf \left\{ x \in ...")
 
 
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Let $\mathbb{T}$ be a [[time scale]]. The forward jump operator $\sigma \colon \mathbb{T} \rightarrow \mathbb{T}$ is defined by the formula  
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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  
$$\sigma(t) := \inf \left\{ x \in \mathbb{T} \colon x > t \right\}.$$
+
$$\sigma(t)=\inf \left\{ x \in \mathbb{T} \colon x > t \right\}.$$
 +
 
 +
=Properties=
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[[Forward jump is rd-continuous]]<br />
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=References=
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* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Time scale|next=Induction on time scales}}: Definition 1.1
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* {{PaperReference|Partial dynamic equations on time scales|2006|Billy Jackson||prev=Multiples of integers|next=Backward jump}}: Appendix
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* {{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

Forward jump is rd-continuous

References