Timeline for Is $f^{-a}$ locally integrable if $f\geq 0$ has a unique stationary point ( a minimum) at which the Hessian is positive definite, $0<a<d/2$
Current License: CC BY-SA 4.0
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| Apr 27, 2023 at 21:11 | history | edited | Medo | CC BY-SA 4.0 |
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| Apr 27, 2023 at 21:06 | history | edited | Medo | CC BY-SA 4.0 |
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| Apr 27, 2023 at 21:02 | comment | added | Fedor Petrov | Ah, only at 0. Sorry, I misread | |
| Apr 27, 2023 at 20:35 | comment | added | Medo | Would you like to elaborate a bit? Condition (3) says the Hessian is positive definite at the origin, so by smoothness, the Hessian is positive definite in some neighborhood of the origin. On that neighborhood the function is strictly convex. What do we infer outside that neighborhood given conditions (1)-(3) ? | |
| Apr 27, 2023 at 8:10 | comment | added | Medo | This is brilliant. But the inequality $f(x)>\delta^{-1} f(\delta x)$ applies to $x$ that lies in convex set that contains $0$ on which $f$ is convex. The question remains : Is the claim ''$f$ is convex '' true and what is the best way to argue that? | |
| Apr 27, 2023 at 8:00 | history | edited | Medo | CC BY-SA 4.0 |
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| Apr 27, 2023 at 7:31 | history | edited | Medo | CC BY-SA 4.0 |
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| Apr 27, 2023 at 7:22 | history | edited | Medo | CC BY-SA 4.0 |
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| Apr 26, 2023 at 20:26 | answer | added | Bazin | timeline score: 1 | |
| Apr 26, 2023 at 19:29 | history | edited | Medo |
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| Apr 26, 2023 at 19:17 | history | undeleted | Medo | ||
| Apr 26, 2023 at 19:15 | history | deleted | Medo | via Vote | |
| Apr 26, 2023 at 19:14 | history | asked | Medo | CC BY-SA 4.0 |