Timeline for Existence of weak limits
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Dec 8, 2011 at 8:00 | history | edited | Harun Šiljak | CC BY-SA 3.0 |
Not a bump of the question - just a correction of my messy update.; Post Made Community Wiki
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| Dec 5, 2011 at 18:26 | history | edited | Harun Šiljak | CC BY-SA 3.0 |
Question update
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| Aug 23, 2010 at 15:25 | history | edited | Willie Wong |
edited tags
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| Jun 17, 2010 at 4:31 | answer | added | Zen Harper | timeline score: 2 | |
| Jun 16, 2010 at 10:22 | history | bounty ended | Harun Šiljak | ||
| Jun 9, 2010 at 10:06 | history | bounty started | Harun Šiljak | ||
| Jun 9, 2010 at 6:35 | history | edited | Harun Šiljak | CC BY-SA 2.5 |
Edit of the reformulation
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| Jun 8, 2010 at 17:48 | history | edited | Harun Šiljak | CC BY-SA 2.5 |
reformulation
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| Jun 8, 2010 at 10:15 | history | edited | Harun Šiljak | CC BY-SA 2.5 |
added the contents of my last comment in the question.
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| Jun 7, 2010 at 19:18 | history | edited | Harun Šiljak | CC BY-SA 2.5 |
description of f and lambda (c/p from the comment)
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| Jun 7, 2010 at 16:09 | comment | added | Harun Šiljak | Yes Pietro, you spotted it well, as I already wrote in the previous question (mathoverflow.net/questions/19398/…). Still, it was shown there that some problems with fixed $\Delta t$ exist. Now when $\Delta t$ varies and goes to zero, I wonder whether we can be certain that existence of RHS implies existence of LHS (note that the converse is almost trivial, since the integral of a test function is a test function itself). | |
| Jun 7, 2010 at 15:33 | comment | added | Pietro Majer | ok, it's the convolution of f with the characteristic function of the interval [-h,h]. (I'd write h or so in place of \Delta t) | |
| Jun 7, 2010 at 13:02 | history | edited | Harun Šiljak | CC BY-SA 2.5 |
nvm
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| Jun 7, 2010 at 13:00 | comment | added | Andrey Rekalo | @Johannes Hahn: why do we need local integrability and cannot just defined the integral in the standard way on test functions? $$\left\langle\phi,\int_{t-\Delta t}^{t+\Delta t}f(\tau)d\tau\right\rangle=\left\langle\int_{t-\Delta t}^{t+\Delta t}\phi(\tau)d\tau,f\right\rangle$$ | |
| Jun 7, 2010 at 12:44 | history | edited | Harun Šiljak | CC BY-SA 2.5 |
Added the condition for $f_\lambda$
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| Jun 7, 2010 at 12:39 | comment | added | Johannes Hahn | The integral in the RHS doesn't make sense for general distributions so the assumption that the $f_\lambda$ are locally integrable should definitively be added. | |
| Jun 7, 2010 at 11:01 | comment | added | Harun Šiljak | $f_\lambda$ are generally distributions from the Schwartz space, parametrized with a real number $\lambda$ - family of Schwartz distributions. In case that the claim does not hold for all Schwartz distributions, it would be interesting to know whether it holds for locally integrable functions. | |
| Jun 7, 2010 at 10:49 | comment | added | Pietro Majer | Wwhere do those $f_\lambda$ live, and what is the dependence on $\lambda$. | |
| Jun 7, 2010 at 9:37 | history | asked | Harun Šiljak | CC BY-SA 2.5 |