Nicolas Essis-Breton
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 Oct 20 comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space? @PrahladVaidyanathan Yes, thank you. I forgot to say that $X$ contains only bounded function. I added it. Oct 20 revised What is the error when approximating $L^2([0,1])$ by a finite dimensional space? added 89 characters in body Oct 20 comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space? @PrahladVaidyanathan I see, I miswrite the max notation. I have corrected it, is it better now? Oct 20 revised What is the error when approximating $L^2([0,1])$ by a finite dimensional space? max Oct 20 comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space? @PrahladVaidyanathan For my understanding, the error is in the orthogonal space. If I use your formula, the error will be too big: for any $f$, the closest $g \in X_n$ to $f$ is $\sum (f,v_i) v_i$, I think. Oct 20 asked What is the error when approximating $L^2([0,1])$ by a finite dimensional space? Oct 18 awarded Revival Oct 18 asked Is there a standard $L^2$ norm for multi-valued function $f:\mathbb R^n \to \mathbb R^n$? Oct 12 accepted Is there a nonstandard characterization of Lipschitz continuity? Oct 11 asked Is there a nonstandard characterization of Lipschitz continuity? Oct 2 awarded Nice Question Oct 1 comment Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$? @copper.hat Your answer shows an other side of the die. Please let it live. Oct 1 accepted Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$? Oct 1 comment Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$? @BobPego The bijection requirement was a first instinct. You made me realized I can forgo it. Thank you for your insightfull comment. Oct 1 asked Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$? Sep 13 awarded Popular Question Sep 6 revised When solving PDEs is there an alternative to interpolation for out-of-grid point? other example Sep 6 revised When solving PDEs is there an alternative to interpolation for out-of-grid point? error in tex Sep 6 asked When solving PDEs is there an alternative to interpolation for out-of-grid point? Aug 31 comment Show that, for a random walk $X$ on $\mathbb Z_2$, $X_\infty$ is independent of the past $\left\{ X_t \right\}_{0\le t<\infty}$ By 'coincides', you mean in distribution: if $X$ is a random walk on $\mathbb Z_2$, as above, and $\left(Y_t\right)$ is an i.i.d sequence with uniform distribution on $\mathbb Z_2$. Then $X_t \buildrel{d}\over = Y_t, \forall t$. I don't see a proof for a stronger mode of convergence.