Timeline for Positive definitness of $f(|x|^\gamma)$, $0<\gamma<1$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2023 at 2:24 | comment | added | Alexey S | @David Roberts I posted the solution BEFORE Iosif posted his | |
| May 2, 2023 at 21:03 | comment | added | Iosif Pinelis | @AlexeyS : How do show this for $s=1$? | |
| May 2, 2023 at 20:24 | comment | added | Alexey S | @TanyaVladi I see it now, A function $\varphi$ is completely monotone on $[0, \infty)$ if and only if $\Phi=$ $\varphi\left(\|\cdot\|^2\right)$ is positive definite and radial on $\mathbb{R}^s$ for all $s$, since the composition of completely monotone and Bernstein is completely monotone we are back to positive definite. | |
| May 2, 2023 at 20:18 | comment | added | Alexey S | math.iit.edu/~fass/603_ch2.pdf | |
| May 2, 2023 at 20:16 | review | Close votes | |||
| May 17, 2023 at 3:09 | |||||
| May 2, 2023 at 20:15 | history | edited | Alexey S | CC BY-SA 4.0 |
added 273 characters in body
|
| May 2, 2023 at 20:10 | comment | added | Iosif Pinelis | Can you give a reference to the theorem you cited? | |
| May 2, 2023 at 19:52 | comment | converted from answer | Alexey S | Since $ e^{-r^{2\gamma} t^2}$ can be represented as a Gaussian mixture, $\phi(r^{\gamma})$ is radial | |
| May 2, 2023 at 19:45 | history | edited | Alexey S | CC BY-SA 4.0 |
added 224 characters in body
|
| May 2, 2023 at 19:40 | history | edited | Alexey S | CC BY-SA 4.0 |
added 224 characters in body
|
| May 2, 2023 at 19:31 | comment | added | Tanya Vladi | as a start, a composition $m(b(x))$ of completely monotone function $m(x)$ and Bernstein function $b(x)$ is completely monotone function; $x^\gamma$, $0<\gamma<1$ is Bernstein function | |
| May 2, 2023 at 18:59 | history | edited | Alexey S | CC BY-SA 4.0 |
deleted 24 characters in body
|
| S May 2, 2023 at 18:58 | review | First questions | |||
| May 2, 2023 at 20:07 | |||||
| S May 2, 2023 at 18:58 | history | asked | Alexey S | CC BY-SA 4.0 |