Timeline for Rate of convergence of the average of an equidistributed sequence
Current License: CC BY-SA 3.0
8 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
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| Feb 13, 2014 at 5:02 | answer | added | Kurisuto Asutora | timeline score: 4 | |
| Dec 5, 2013 at 22:22 | comment | added | smyrlis | If the irrational is fixed, then $f$ can be restricted according to the measure of irrationality of the irrational. I need an estimate which holds for all irrationals, for $f$ real analytic. Apparently, we do not expect to have a uniform bound, for all irrationals. I am asking for a possibly optimal (sublinear) order of growth of this sequence, which holds for all irrationals (with different constants). | |
| Dec 5, 2013 at 12:45 | comment | added | Ian Morris | Could you perhaps be more specific about the order of quantifiers? That is, do you want an estimate which works for fixed $f$ and for all irrational $\alpha$, or an estimate which works for fixed irrational $\alpha$ and all $f$ within a given smoothness class, or...? | |
| Dec 5, 2013 at 11:53 | comment | added | smyrlis | Does any of these inequalities (Denjoy-Koksma & Koksma-Hlawka) improve the estimate for the sequence of the partial sums? Or, does it suggest this estimate is the optimal one? | |
| Dec 5, 2013 at 11:11 | comment | added | Asaf | And of course the related Koksma–Hlawka inequality | |
| Dec 5, 2013 at 11:06 | comment | added | Asaf | You are more or less asking about the Denjoy-Koksma inequality | |
| Dec 5, 2013 at 10:29 | history | asked | smyrlis | CC BY-SA 3.0 |