Timeline for Approximation of Hölder continuous functions "from below"
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 11, 2023 at 2:12 | history | edited | LSpice | CC BY-SA 4.0 |
Link to answer
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| Apr 10, 2023 at 22:26 | comment | added | Nik Weaver | Yes, if $\alpha < \beta$ then every $\alpha$-Holder function is not only $\beta$-Holder, but even $\beta$-locally flat. So you are right, anything in $C^\alpha$ can be approximated in $\beta$-Holder norm by $C^\infty$ functions. (That's not to say approximable from below, though.) | |
| Apr 10, 2023 at 21:46 | comment | added | António Borges Santos | thank you, does this actually mean the approximation I asked for is possible in every $C^{\beta}$ norm with $\beta< \alpha$? | |
| Apr 10, 2023 at 15:30 | history | answered | Nik Weaver | CC BY-SA 4.0 |