  Using ultra-precise data from space instrumentation we found that the
underlying functions of stellar light curves from some AF pul- sating stars are
non-analytic, and consequently their Fourier expansion is not guaranteed. This
result demonstrates that periodograms do not provide a mathematically
consistent estimator of the frequency content for this kind of variable stars.
More importantly, this constitutes the first counterexample against the current
paradigm which considers that any physical process is described by a contin-
uous (band-limited) function that is infinitely differentiable.

Solar and Stellar Astrophysics