Timeline for Functions for which $\lambda f(x)=f(\alpha_\lambda x + \beta_\lambda)$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 9 at 13:33 | vote | accept | gmvh | ||
| Feb 3 at 18:21 | comment | added | Aleksei Kulikov | @gmvh since all the ones I constructed are multiplicative, the continuous ones are only of the form $c sign(x)|x|^s$ which you already know of. | |
| Feb 3 at 17:05 | comment | added | gmvh | @AlekseiKulikov interesting! I wonder how many of these are continuous. | |
| Feb 3 at 3:40 | answer | added | Aleksei Kulikov | timeline score: 1 | |
| Feb 3 at 3:14 | comment | added | Aleksei Kulikov | It seems to me I can construct $2^{\mathfrak{c}}$ such functions (which is obviously the biggest it can be) for $S =\mathbb{R}$ and even with $\beta_\lambda = 0$ always by taking logarithms and writing the abelian group $\mathbb{R}$ as a direct sum of $\mathfrak{c}$-many $\mathbb{R}$'s. | |
| Feb 2 at 11:08 | comment | added | gmvh | @Nandor Well, non-empty is an obvious requirement to make this meaningful. In fact, I would like $S$ to contain an interval containing $1$, which I added. But if there are cases for another non-empty $S$, I'd be interested in those, as well. | |
| Feb 2 at 11:06 | history | edited | gmvh | CC BY-SA 4.0 |
Reply to comment by Nandor
|
| Feb 2 at 9:50 | comment | added | Antonius | Can you be more specific as to what you want $S$ to look like? The empty set would always do... | |
| Feb 2 at 9:17 | history | edited | gmvh | CC BY-SA 4.0 |
Minor correction
|
| Feb 2 at 8:15 | history | asked | gmvh | CC BY-SA 4.0 |