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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 1 year, 1 month |
| seen | yesterday | |
| stats | profile views | 51 |
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May 16 |
revised |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? fixed error |
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May 14 |
accepted | Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? |
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May 14 |
revised |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? fixed erroneous statement |
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May 14 |
answered | Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? |
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May 14 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? I found a proof to this and my more general question that is actually not fourier analytic. Ill post in a day or two when I get the chance. |
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May 8 |
comment |
Diffeomorphism of open intervals in $\mathbb{R}$ with specified values Yes @Berci is correct, I just forgot to say that. I edited the statement to include the clarification. |
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May 8 |
revised |
Diffeomorphism of open intervals in $\mathbb{R}$ with specified values clarification |
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May 8 |
asked | Diffeomorphism of open intervals in $\mathbb{R}$ with specified values |
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May 8 |
revised |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? Added tag |
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May 7 |
revised |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? added tag |
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May 7 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? No worries I'm in the same boat. Ill post a solution if I figure it out in the meantime. |
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May 6 |
awarded | Caucus |
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May 6 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? This may be a dumb question, but what ensures that $\widehat{G}$ is in $L_2[0,1]$? It is certainly in $L_1[0,1]$, but when I try to calculate its 2-norm, I can't seem to find a good inequality. By definition, $\int_0^1|\widehat{G}(x)|^2dx=\int_0^1\left|\sum_n\widehat{g}(x+n)\right|^2dx$. But I don't necessarily see how to bound this by something useful after some effort. |
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Apr 29 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? Thanks for your post, I finally went through all of it to check. Forgetting the simple fact that lead to your conclusion that $\sum|g(n)|^2=\|\widehat{G}\|_2^2$ cost me no small amount of time, but I managed to dig into the recesses of my Fourier analysis knowledge to remember the easy $L_2$ theory finally. |
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Apr 28 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? There was a counter example construction posted earlier but he claimed that the derivative was square integrable and I was not so sure based on the construction. |
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Apr 28 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? That is a good comment, because IF this is true the proof must use in a crucial way that the derivative is in $L_2$ because if $g$ is even continuous and only in $L_2$ not sobolev then the conclusion fails. |
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Apr 27 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? Sorry just needed one more step. It would seem we have $\sum_n |g(n)|^2\leq \sum_n\int_0^1|g(x+n)|^2dx=\|g\|_{L_2}$? |
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Apr 26 |
comment |
Is $\{g(n)\}_{n\in\mathbb{Z}}\in\ell_2$ if $g$ is a Sobolev function on the real line? Could you clarify your hint a little? I understand than the $L_2$ norm of $g$ is equal to $\int_0^1 \sum_n |g(x+n)|^2 dx$, but I am not sure what you are getting at. |
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Apr 26 |
comment |
Derivatives using the Limit Definition Always consider multiplying by the conjugate when you have imaginary numbers or radicals in the expression! |
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Apr 26 |
suggested | suggested edit on Derivatives using the Limit Definition |
