Difference between revisions of "Hilger alternating axis"

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The Hilger alternating axis is defined by
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The Hilger alternating axis is defined for $h>1$ by
$$\mathbb{A}_h = \left\{z \in \mathbb{C}_h \colon z \in \mathbb{R}, z < -\dfrac{1}{h} \right\},$$
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$$\mathbb{A}_h = \left\{z \in \mathbb{R} \colon z < -\dfrac{1}{h} \right\},$$
where $\mathbb{C}_h$ is the [[Hilger complex plane]].
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and for $h=0$ we let $\mathbb{A}_0=\emptyset$.  
  
 
=Properties=
 
=Properties=
  
 
=References=
 
=References=
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* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Hilger real axis|next=Hilger circle}}: 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=Hilger real axis|next=Hilger circle}}: 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=Hilger real axis|next=Hilger circle}}: Definition $2.2$
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[[Category:Definition]]
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<center>{{:Hilger complex plane footer}}</center>

Latest revision as of 15:38, 21 January 2023

The Hilger alternating axis is defined for $h>1$ by $$\mathbb{A}_h = \left\{z \in \mathbb{R} \colon z < -\dfrac{1}{h} \right\},$$ and for $h=0$ we let $\mathbb{A}_0=\emptyset$.

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