Timeline for Approximating a strictly increasing non-negative function on a non-negative domain by polynomials with non-negative coefficients
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2023 at 14:06 | answer | added | Saúl RM | timeline score: 2 | |
| Apr 5, 2023 at 4:12 | comment | added | Peter O. | @Saúl RM : You should post your comment as an answer to keep this site from seeing this question as unanswered. | |
| Oct 15, 2022 at 6:40 | comment | added | Jack | Okay, got it, thanks. | |
| Oct 15, 2022 at 2:23 | comment | added | Saúl RM | The problem of which functions $f:[0,1]\to\mathbb{R}$ can be approximated by polynomials with non negative coefficients has already been studied: as theorem 2 of this paper states, a continuous function $f:[0,1]\to\mathbb{R}$ is a pointwise limit of polynomials with non negative coefficients iff $f(x)=\sum_{n=0}^\infty a_nx^n$ for some non negative sequence $a_n$ such that $\sum a_n<\infty$. | |
| Oct 14, 2022 at 20:05 | comment | added | Qiaochu Yuan | As mathworker21 alludes to, this is impossible for, say, $f(x) = 4x - x^2$ because a uniform limit of convex functions is convex. | |
| Oct 14, 2022 at 19:52 | comment | added | mathworker21 | what if $f$ is concave? | |
| Oct 14, 2022 at 19:42 | history | edited | Jack | CC BY-SA 4.0 |
edited body
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| Oct 14, 2022 at 19:38 | history | edited | Jack | CC BY-SA 4.0 |
added 4 characters in body
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| S Oct 14, 2022 at 19:30 | review | First questions | |||
| Oct 15, 2022 at 7:51 | |||||
| S Oct 14, 2022 at 19:30 | history | asked | Jack | CC BY-SA 4.0 |