Difference between revisions of "Hilger complex plane"
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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 $\mathbb{C}_0=\mathbb{C}$. | and for $h=0$, we let $\mathbb{C}_0=\mathbb{C}$. | ||
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 $2.2$
