Toronto Math Forum

APM346-2018S => APM346--Lectures => Topic started by: Jingxuan Zhang on March 06, 2018, 08:06:25 PM

Title: Fourier coefficients
Post by: Jingxuan Zhang on March 06, 2018, 08:06:25 PM
Could anyone kindly inform me one more time the origin of the scalar multiple in finding Fourier coefficients? I know these are supposed be inner product, but I don't remember a scaling there.
Also, chap 4.3 remark 2 has some obvious typo. (Somewhere 2's in $L^2$'s are missing).
Title: Re: Fourier coefficients
Post by: Victor Ivrii on March 07, 2018, 03:21:09 AM
Well, it is $1/\|X_n\|^2$ with $X_n$ corresponding basis function.
Title: Re: Fourier coefficients
Post by: Jingxuan Zhang on March 07, 2018, 06:58:39 AM
As if when we do the projection of $b$ on $a$ in Euclidean space, the coefficient is given by $a\cdot b / ||a||^2$?
Title: Re: Fourier coefficients
Post by: Victor Ivrii on March 07, 2018, 07:58:42 AM
Exactly. I told you so