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
What norm? The [tex]L^2[/tex]-norm can be expressed, and it is the square root of the sum of the squares of the coefficients.
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.
well, it's only the L^{2} norm (a measure of energy) in which the L^{2} norm of the time-domain function (over one period) is equal to the L^{2} of the frequency-domain data (the Fourier coefficients). i think the L^{2} norm of your f(x) is a^{2} + b^{2} + c^{2}.