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> This is impossible with sums of continuous periodic functions, such as Fourier series, because continuous periodic functions are bounded, while x^2 is unbound
by vbuterin 13y ago
> This is impossible with sums of continuous periodic functions, such as Fourier series, because continuous periodic functions are bounded, while x^2 is unbounded.
But infinite sums of continuous periodic functions are not necessarily bounded: sin(x) + sin(x/2) + sin(x/4) + ... is an example. So there has to be something else to the proof.
- ot 13y agoYou are right, but I was referring to either finite sums or Fourier series, your example is not one because sum of the squares of the coefficients is infinite. I don't know what can be said about arbitrary countable/uncountable sums of continuous periodic functions.