Timeline for Polynomial approximation for square root function with fast convergence and bounded coefficients
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 21, 2022 at 18:46 | comment | added | Andrew Hardy | What about if you restrict to the positive real numbers, ie $\forall x \in [\delta,1]$? Can you restrict the output of $f$ to be real? Or if not, why not? | |
| Jul 30, 2021 at 12:52 | comment | added | user44143 | Thanks! It is a hundred years old but new to me. | |
| Jul 30, 2021 at 12:51 | history | edited | user44143 | CC BY-SA 4.0 |
added graphic
|
| Jul 29, 2021 at 23:56 | comment | added | fedja | @MattF. The statement is just as I've written. Usually it is stated on the unit circle for the value at $0$: If $F$ is an analytic function in the disk continuous up to the boundary and $L$ is an arc on the unit circumference $\mathbb T$, then $|F(0)|\le [\max_L |F|]^{m(L)}[\max_{\mathbb T\setminus L}|F|]^{1-m(L)}$ where $m(L)=|L|/(2\pi)$. The case of the general simply connected domain with an arbitrary point is obtained by applying a conformal mapping. It is just about subharmonicity of $\log|F|$, nothing fancy. See encyclopediaofmath.org/wiki/Two-constants_theorem | |
| Jul 29, 2021 at 7:35 | comment | added | user44143 | Can you provide a statement or reference for the two-constant lemma? | |
| Jul 29, 2021 at 1:37 | history | answered | fedja | CC BY-SA 4.0 |