Timeline for Reference request: Arzela-Ascoli theorem for smooth Hölder norms
Current License: CC BY-SA 3.0
10 events
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| Jun 1, 2018 at 22:39 | review | Close votes | |||
| Jun 2, 2018 at 19:21 | |||||
| May 29, 2012 at 14:58 | history | edited | Pietro Majer | CC BY-SA 3.0 |
edited title
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| Jan 13, 2011 at 12:51 | comment | added | Igor Belegradek | Sure, everything should be obtainable by straighforward iteration of the $C^0$ Arzela-Ascoli. I was just hoping to find some place where it is written. | |
| Jan 13, 2011 at 4:25 | comment | added | Deane Yang | The standard version of Arzela-Ascoli theorem says an equicontinuous family of functions is compact in the $C^0$ topology. I believe that it is straightforward to show that a uniform $C^\alpha$ bound implies equicontinuity. I also believe it is reasonably straightforward extend this argument to the general case. But I haven't worked out the details. | |
| Jan 13, 2011 at 2:10 | comment | added | Igor Belegradek | Deane, I don't have the books handy, and won't get to them before Friday (due to snowstorm) but what I see in google.books while searching them isn't promising. Anyway, I agree that these should be the first books to look at, thanks. | |
| Jan 13, 2011 at 1:53 | comment | added | Deane Yang | Maybe a book that explains Schauder estimates for elliptic PDE's? Gilbarg and Trudinger? Or the book by L. C. Evans? | |
| Jan 13, 2011 at 1:12 | history | edited | Yemon Choi |
added func-an tag
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| Jan 12, 2011 at 23:49 | comment | added | Igor Belegradek | There are various versions of Arzela-Ascoli, but typically one starts with a sequence of functions that has a uniform bound on $C^{k,\alpha}$ norm, an one want to extract a subsequence converging to in $C^{m,\beta}$ norm where $m+\beta<k+\alpha$, and one also gets information about regularity of the limit. There are also some subtleties when $\alpha = 0$. I found that I do not have a sufficiently firm grip on these matters. | |
| Jan 12, 2011 at 23:26 | comment | added | Deane Yang | Not sure I understand. Could you provide the precise statement that you want a reference for? | |
| Jan 12, 2011 at 21:45 | history | asked | Igor Belegradek | CC BY-SA 2.5 |