Difference between revisions of "Hilger complex plane"
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(Created page with "Let $h>0$ be fixed. We define the Hilger complex plane to be $$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq \dfrac{1}{h} \right\}.$$") |
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Let $h>0$ be fixed. We define the Hilger complex plane to be | Let $h>0$ be fixed. We define the Hilger complex plane to be | ||
| − | $$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq \dfrac{1}{h} \right\}.$$ | + | $$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq -\dfrac{1}{h} \right\},$$ |
| + | and for $h=0$, we let $\mathbb{C}_0=\mathbb{C}$. | ||
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| + | =Properties= | ||
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| + | =References= | ||
| + | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=|next=Hilger real axis}}: Definition 2.2 | ||
| + | *{{PaperReference|A generalized Fourier transform and convolution on time scales|2008|Robert J. Marks II|author2=Ian A. Gravagne|author3=John M. Davis|prev=Causal time scale|next=Hilger real axis}}: Definition $2.2$ | ||
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| + | [[Category:Definition]] | ||
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| + | <center>{{:Hilger complex plane footer}}</center> | ||
Latest revision as of 12:45, 6 June 2023
Let $h>0$ be fixed. We define the Hilger complex plane to be $$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq -\dfrac{1}{h} \right\},$$ and for $h=0$, we let $\mathbb{C}_0=\mathbb{C}$.
Properties
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (next): Definition 2.2
- Robert J. Marks II, Ian A. Gravagne and John M. Davis: A generalized Fourier transform and convolution on time scales (2008)... (previous)... (next): Definition $2.2$
