Timeline for Approximating a function by fractional powers
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 21, 2021 at 12:53 | comment | added | Alexandre Eremenko | @memorial: I wrote "roughly speaking"; the condition I wrote assumes $r_k\to\infty$ which is the most interesting case. | |
| Oct 21, 2021 at 6:29 | comment | added | memorial | This version of the Müntz-Szasz theorem is faulty. The actual condition is $$\sum \dfrac{\lambda_n}{{\lambda_n}^2+1}=\infty$$ when $((\lambda_n)$ is a sequence of distinct positive numbers. This allows for much more subtle behaviour. (Off topic comment: it is my opinion that the full glory of the result is only revealed when one allows complex exponents. Then the divergence of $$\sum(1-|\frac{\lambda_n-1}{\lambda_n+1}|)$$ suffices for denseness. This allows for much more exotic examples of "slow convergence to the boundary"). | |
| Nov 3, 2012 at 13:49 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |