Hilger alternating axis

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 $\mathbb{A}_0=\emptyset$.

References

• Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (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 $2.2$

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