Timeline for Markov-Bernstein like inequalities for monotone polynomials
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2014 at 3:05 | comment | added | fedja | The hope is there only as long as you restrict yourself to the formulations and never look into the proofs. However, if you take any explicit convolution type polynomial approximation operator (like replanting the function to the circle and taking the Fejer sum, say), you will realize that the width of its kernel support is $1/d$ for all practical purposes, so an attempt to approximate the function that is $0$ for $x<0$ and $1$ for $x>0$ will result in a non-decreasing polynomial of degree $d$ that jumps from nearly $0$ to nearly $1$ within the distance of order $1/d$. | |
| Jun 11, 2014 at 16:36 | comment | added | NoamL | Thanks for your answer! As I said I am especially interested at bounding $P'$ near $0$. There is still hope for improvements at that aspect. | |
| Jun 11, 2014 at 15:13 | history | answered | user64494 | CC BY-SA 3.0 |