Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
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no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.
Joseph Fourier was the French mathematician and physicist after whom Fourier Series, Fourier's Law, and the Fourier Transform were named. He is commonly credited with discovering the greenhouse effect.
An aperiodic signal cannot be represented using fourier series because the definition of fourier series is the summation of one or more (possibly infinite) sine wave to represent a periodicsignal. Since an aperiodic signal is not periodic, the fourier series does not apply to it. You can come close, and you can even make the summation mostly indistinguishable from the aperiodic signal, but the math does not work.
Ozzie Nelson, sons Ricky and David
The television series program, Sabrina, the Teenage Witch, was created by Nell Scovell and developed by Jonathan Schmock, while airing weekly on ABC and WB broadcasting networks.