Dear Eckard ,
Could you elaborate the meaning of the - in these tranformations of fourier please? .
I think you make a big error when you don't consider the irreversibility and the linearity of the physical dynamic .
Some parameters are fundamentals and linears .
And the time is a constant of this system .You can take the micro, the meso, or the macro point of vue ,these fundamentals don't change in their linearity .The quantum mechanic is correlated with the cosmological dynamic, with of course different parameters but the thermodynamic laws and the constants ,relatively perceptibles,the time rest invariants .
You can play with the pression ,the volume ,the temperature ,the density ,the mass ,the energy ,the entropy ,but not with our linearities ,reals in our physicality.
The fact to analyze a system like that is in contradiction with the evolution point of vue and its irreversibility of creations on this line time .
This essential piece can't change its state ,fundamentals everywhere in all centers of interest.
The maths are a very best tools ,probably the best for analyze our physicality .But we can't play without rationality .If the infinity ,the -,the 0 more the imaginaries are inserted in an extrapolation of the mind where the time isn't considered,thus how can you arrive to a good understanding of your physical world and its specific laws .
Let's take a fourier serie during an harmonic analyze,what is your domain ,your intrinsic laws,the periodicity,the variables ....you can take bessel too for an analytic harmonic approach ,...in the physicality we can't insert the numbers what we want ,or the domain what we want ,without an irreversible evolutive system ,what is the real sense of an analyze if the essentials and the fundamentals axioms aren't considered?
It is impossible to encircle thus .
You know ,I am ok with math if and only if they synchronize the real physicality and its irreversible linearity .
It exists limits in all physical systems and the irreversibility of the gravity ,mass ,time ....are an evidence in a whole analyze.
Best Regards
Steve