Timeline for Does this sequence span $L^2$?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jun 13, 2010 at 12:18 | comment | added | Victor Protsak | I am not familiar with the notion of stability, but don't you need to assume that $\|f_n\|=1$ in the inequality that defines it? (Presumably, it's invariant under rescalings.) Also, what happened to the exponential factor in the second displayed formula? | |
| Jun 11, 2010 at 15:37 | comment | added | Matthew Daws | Well, it is was ``stable'' then by definition, there should be a constant $c>0$ with $\sum_n |\langle f_n,g\rangle|^2 \geq c \|g\|^2_2$, which Philipp has shown can't happen for this sequence $(f_n)$. | |
| Jun 11, 2010 at 14:00 | comment | added | Willie Wong | ... I meant, of course, what you mean by "this implies instability"? (Sorry about the typo.) | |
| Jun 11, 2010 at 13:57 | comment | added | Willie Wong | But if $\lambda \to 0$, does the norm of $g$ not also approach 0? Can you clarify what you mean by "this implies stability"? | |
| Jun 11, 2010 at 9:56 | history | answered | Philipp | CC BY-SA 2.5 |