Timeline for Constructing an L2-space with a given orthonormal basis
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 12, 2011 at 13:16 | answer | added | Vagabond | timeline score: 6 | |
| Nov 11, 2011 at 19:00 | comment | added | Will Sawin | The integral you are setting to $0$ is just the $L_2$ dot product of $e^{it (x_n-x_m)$ and $\lambda(t)$ (if $\lambda$ can be represented by an $L_2$ function). Thus, there is a solution if (but not necessarily only if) the functions $e^{it(x_n-x_m)}$ do not span a dense subspace of $L^2$. Note, for instance, that the functions $e^{it(n-m)}$, $N\neq m$, span the space of functions with integral $0$. | |
| Nov 11, 2011 at 17:38 | history | asked | puerilescribble | CC BY-SA 3.0 |