Timeline for Is the minimal modulus of continuity of a $C^k$ function also $C^k$?
Current License: CC BY-SA 4.0
20 events
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| Jul 19, 2022 at 16:41 | comment | added | Christophe Leuridan | @Iosif Pinellis Yes, you are right. I will remove the comment. | |
| Jul 19, 2022 at 15:04 | comment | added | Iosif Pinelis | @ChristopheLeuridan : I am not sure what you mean by "a boundary problem". In the main example in this answer, the effect is caused by something happening in an interior. Also, an example with the (horizontally rescaled) $\cos$ was already given in the beginning of the answer -- but then the effect was due to something happening indeed at a boundary point of the range of values of $\omega_f$. The main example in the answer fixes this non-desired only-at-the-boundary thing. | |
| Jul 19, 2022 at 12:33 | history | bounty ended | Nate River | ||
| Jun 19, 2022 at 3:52 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 19, 2022 at 3:50 | comment | added | Iosif Pinelis | @NateRiver : Thank you for your appreciation. | |
| Jun 18, 2022 at 5:10 | comment | added | Nate River | Humans are indeed pretty strong visually… | |
| Jun 18, 2022 at 5:09 | comment | added | Nate River | Extremely impressive! I really like this quote: “Even though details of calculations will be provided below, one might say that the stated properties of the function $f$ are almost obvious from the picture, except perhaps for the specific value of $\Delta$. Our visual apparatus is a powerful computer!” | |
| Jun 17, 2022 at 22:07 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 21:50 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 18:11 | comment | added | Iosif Pinelis | I have completed the details for the counterexample for the domain $[0,1]$. | |
| Jun 17, 2022 at 18:09 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 17:58 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 17:48 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 16:08 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 15:40 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 15:22 | comment | added | Iosif Pinelis | The first of these two examples can be modified for the domain $[0,1]$. I will write it up. | |
| Jun 17, 2022 at 15:16 | vote | accept | Nate River | ||
| Jun 17, 2022 at 15:16 | comment | added | Nate River | Ah, of course there will be a kink once the $\delta$ exceeds the functions’ max deviation. I wonder if it is as smooth as $f$ on its natural domain $(0, \sup f - \inf f]$ though, like @ChristianRemling suggests. | |
| Jun 17, 2022 at 14:52 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 17, 2022 at 13:51 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |