- Thread starter
- #1

I know this has to do with the uniqueness of the Fourier coefficients, but I don't know how to solve it.

Thanks!

- Thread starter Markov
- Start date

- Thread starter
- #1

I know this has to do with the uniqueness of the Fourier coefficients, but I don't know how to solve it.

Thanks!

- Admin
- #2

- Jan 26, 2012

- 4,197

Sounds an awful lot like the Riemann-Lebesgue Lemma. Are the tools of Lebesgue integration available to you?

I know this has to do with the uniqueness of the Fourier coefficients, but I don't know how to solve it.

Thanks!

- Moderator
- #3

- Feb 7, 2012

- 2,725

This requires some fairly heavy machinery. One method is to use Fejér's theorem, which says that $f$ is the uniform limit of the Cesàro sums $s_n(f)$ of its Fourier series. If all the Fourier coefficients of $f$ are zero then $s_n(f)=0$ for all $n$, and hence $f=0.$

I know this has to do with the uniqueness of the Fourier coefficients, but I don't know how to solve it.

Thanks!