Inverse cylinder transformation

Let $\mathbb{T}$ be a time scale. We define the inverse cylinder transformation $\xi_h \colon \mathbb{Z}_h \rightarrow \mathbb{C}_h$, where $\mathbb{Z}_h$ denotes the cylinder strip and $\mathbb{C}_h$ denotes the Hilger complex plane, and is defined by the formula $$\xi_h^{-1}(z)=\dfrac{e^{zh}-1}{h}.$$

References

• Robert J. Marks II, Ian A. Gravagne and John M. Davis: A generalized Fourier transform and convolution on time scales (2008)... (previous)... (next): $(2.3)$