Fourier transform of a tetration function

[Ivars]

what does lightspeed has to do with tetration or fourier transform ?

Shorter: What is the Fourier transform of t^t or other hyperfast operations?

Does there exist set of complex periodic functions (not necesserily e^+-Iwt) whose linear summation (integration) gives t^t and faster hyperoperations?

Mechanisms that happen faster than exponential growth could well be employed in various physical mechanisms, like phase transform.

@Bo: Thank You!

Ivars