Expressing Function Norm Using Fourier Coefficients

[sristi89]

Hi,

I was wondering if it is possible to express the norm of a function in terms of Fourier coefficient. If so, how do you go through it if given a particular function.

Thanks

 

[jostpuur]

What norm? The L^2-norm can be expressed, and it is the square root of the sum of the squares of the coefficients.

 

[sristi89]

Here is a sample question:

What are the Fourier coefficients of the function f(x)=ae^(-ix)+b+ce^(ix)? And express the norm in terms of Fourier coefficients.

They don't mention if it is the L^2 norm or not.

 

[rbj]

well, it's only the L² norm (a measure of energy) in which the L² norm of the time-domain function (over one period) is equal to the L² of the frequency-domain data (the Fourier coefficients).

i think the L² norm of your f(x) is a² + b² + c².