Marks-Gravagne-Davis Fourier transform as a delta integral with classical exponential kernel

Theorem

If $0 \in \mathbb{T}$, then the Marks-Gravagne-Davis Fourier transform obeys $$\mathscr{F}_{\mathbb{T}}\{f\}(z;0) = \displaystyle\int_{-\infty}^{\infty} f(t)e^{-2i\pi zt} \Delta t.$$

References

• Robert J. Marks II, Ian A. Gravagne and John M. Davis: A generalized Fourier transform and convolution on time scales (2008)... (previous): Section 3 (3.1)