Quick question: If a Fourier series is uniformly convergent should the term-by-term Laplace transform of the series equal the result of the periodic function theorem for the Laplace transform?
2026-03-30 15:36:46.1774885006
Fourier series: term-by-term Laplace transform.
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No, because the Fourier series defines a periodic function for $-\infty<t<\infty$, whereas the periodic function theorem of the Laplace transform refers to functions which are zero for $t<0$. The Laplace transform of a periodic function (defined for $-\infty<t<\infty$) does not exist.