Timeline for Boundedness from convergence of some demeaned sequence
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 20 at 0:29 | vote | accept | user108 | ||
| Mar 20 at 0:11 | answer | added | Aleksei Kulikov | timeline score: 3 | |
| Mar 19 at 23:35 | comment | added | user108 | I was thinking of something like $b_n$ decaying at some rate dependent on $n$, like $1/n$. But the necessary and sufficient condition you suggested sounds just perfect! Can you please give detail in the answer? | |
| Mar 19 at 23:31 | comment | added | Aleksei Kulikov | In fact, I can show that $a_n$ are bounded if and only if $b_n$ are bounded and partial sums of $\sum \frac{b_n}{n}$ are uniformly bounded. Is it good enough for you? | |
| Mar 19 at 23:24 | comment | added | Aleksei Kulikov | The answer to the first question is no, for example $a_n = \log \log (n)$. What type of conditions on $b_n$ are you interested in? | |
| Mar 19 at 22:55 | history | asked | user108 | CC BY-SA 4.0 |