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
$$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq \dfrac{1}{h} \right\}.$$
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$$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq -\dfrac{1}{h} \right\},$$
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and for $h=0$, we let $\mathbb{C}_0=\mathbb{C}$.
  
 
=Properties=
 
=Properties=
  
 
=References=
 
=References=
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* {{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 $2.2$
 
*{{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

Hilger complex plane and friends

$\Huge\mathbb{A}_h$
Hilger alternating axis
$\Huge\mathbb{I}_h$
Hilger circle
$\Huge\mathbb{C}_h$
Hilger complex plane
$\Huge\mathrm{Im}_h$
Hilger imaginary part
$\Huge\mathring{\iota}$
Hilger pure imaginary
$\Huge\mathbb{R}_h$
Hilger real axis
$\Huge\mathrm{Re}_h$
Hilger real part