Timeline for Coefficients from Stone–Weierstrass versus Fourier transform
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 24, 2010 at 23:20 | comment | added | Dorian | I'm concerned with $f \in L^1([0,1])$ but not in $L^2([0,1])$ so that you can't just use the $L^2$ structure. | |
| Aug 24, 2010 at 19:38 | comment | added | Otis Chodosh | By Holder's inequality on $[0,1]$, $\Vert f \Vert_{L^1} \leq \Vert f \Vert_{L^2}$ so what I have shown is that if you started with a f that was actually in L2 , then you can replace the L2 convergence statements with L1 convergence. | |
| Aug 24, 2010 at 18:59 | comment | added | Dorian | You hae misunderstood my question. I'm concerned with $L^1([0,1])$. Of course we have a fourier series in $L^2([0,1])$ but my point is that we get coefficients regardless and we should get convergence in $L^1([0,1])$ as well for certain coefficients (not the fourier coefficients though a priori if our function is not $L^2([0,1])$). | |
| Aug 24, 2010 at 18:43 | history | answered | Otis Chodosh | CC BY-SA 2.5 |