Timeline for Gaps between roots of trigonometric polynomials
Current License: CC BY-SA 3.0
15 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| S Aug 22, 2014 at 19:59 | history | bounty ended | Kirill | ||
| S Aug 22, 2014 at 19:59 | history | notice removed | Kirill | ||
| Aug 22, 2014 at 19:59 | vote | accept | Kirill | ||
| Aug 20, 2014 at 5:39 | history | edited | Kirill | CC BY-SA 3.0 |
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| Aug 18, 2014 at 3:58 | comment | added | John Jiang | You could also let $z=e^{it}$ and write your trig polynomial function as an algebraic polynomial function $F$ in $z$. Then looking at the discriminant of $F$ maybe helpful. Another possibly unrelated note: Nazarov has proved some generalization of Remez's inequality, that bounds the amount of time a trig polynomial stays around 0 in terms of its degree. | |
| Aug 17, 2014 at 8:11 | answer | added | Igor Khavkine | timeline score: 6 | |
| S Aug 17, 2014 at 0:23 | history | bounty started | Kirill | ||
| S Aug 17, 2014 at 0:23 | history | notice added | Kirill | Draw attention | |
| Aug 15, 2014 at 18:06 | history | edited | Kirill | CC BY-SA 3.0 |
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| Aug 11, 2014 at 11:06 | history | edited | Kirill | CC BY-SA 3.0 |
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| Aug 11, 2014 at 9:44 | comment | added | Kirill | @fedja I edited the question to try and explain myself better. Please let me know if it is still unclear. | |
| Aug 11, 2014 at 9:43 | history | edited | Kirill | CC BY-SA 3.0 |
Tried to explain the question better.
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| Aug 9, 2014 at 11:38 | comment | added | fedja | It is a little bit unclear what exactly you are asking because the word "general" may mean about 100 different things. The most trivial interpretation is that $c_k$ are standard i.i.d. complex Gaussians ($k>0$); show that, with probability close to $1$, .... This certainly has been done but I have no idea if this is even remotely close to what you are looking for except your last sentence shows that the answer is somewhat more likely to be "no" than "yes". Can you elaborate a bit on what you would consider a useful characterization? | |
| Aug 9, 2014 at 3:42 | history | asked | Kirill | CC BY-SA 3.0 |