Timeline for Characterization of differentiability
Current License: CC BY-SA 4.0
11 events
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| Sep 20, 2021 at 13:21 | history | edited | Kacper Kurowski | CC BY-SA 4.0 |
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| Sep 20, 2021 at 13:11 | history | edited | Kacper Kurowski | CC BY-SA 4.0 |
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| Sep 19, 2021 at 10:13 | comment | added | Kacper Kurowski | @PietroMajer Also, the idea of said limiting process is why I expect the assumption for $Y$ to be a Banach space to be useful. I think one would need to work with some Cauchy sequences and “build” the differential using their convergence. Moreover, I think that there might be a function, which has values in some normed space $Z$, which is not differentiable in $Z$, but differentiable in the completion of $Z$. Hence, making the assumption of the codomain being a Banach space necessary. | |
| Sep 19, 2021 at 10:00 | comment | added | Kacper Kurowski | @PietroMajer I think the differential $d_x f$ might be reconstructed from the "parametrised segments" $\gamma_{f(x)}^{f(y)}$ by some limiting process. The idea being that rays from $f(x)$ passing through $f(y)$ for $y$ in some neighbourhood of $x$ approach the graph of the differential (translated so that point $(0,0) \in X \times Y$ goes to $( x, f(x) )$ ) as the neighbourhood get smaller | |
| Sep 19, 2021 at 7:49 | history | edited | YCor |
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| Sep 19, 2021 at 4:51 | history | edited | LSpice | CC BY-SA 4.0 |
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| Sep 19, 2021 at 4:19 | comment | added | Pietro Majer | How would you define df (x) for a function satisfying these conditions then? | |
| Sep 18, 2021 at 23:14 | history | edited | Kacper Kurowski | CC BY-SA 4.0 |
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| Sep 18, 2021 at 22:39 | history | edited | Kacper Kurowski | CC BY-SA 4.0 |
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| Sep 18, 2021 at 22:31 | history | edited | Kacper Kurowski | CC BY-SA 4.0 |
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| Sep 18, 2021 at 22:26 | history | asked | Kacper Kurowski | CC BY-SA 4.0 |