Timeline for Proving that a specific kernel is positive definite
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2020 at 21:19 | comment | added | user72012 | $-(x+y)^\alpha$ is nd when $\alpha \in [1,2]$ only, right? | |
| May 22, 2014 at 16:56 | comment | added | Suvrit | Indeed, proving strict positive definiteness requires more work (apparently, I only read the first sentence of your original question and the formula for the kernel function but did not notice the strict inequality!) Once I get a chance, I'll try to update with pointers that may help in establishing the strictness. | |
| May 22, 2014 at 12:57 | comment | added | cs89 | Sorry to come back to this. I have read (BCR) and I think I understand the proofs. My initial question included a strict inequality. I am having a hard time proving it, because I think one cannot derive the strict positivity of an integral operator from properties of the matrices. Indeed, working on matrices implies that you must take some kind of a limit to recover results on the integral operator. And, of course, this limit will not preserve any kind of strict inequality you may have obtained on the matrices. | |
| May 14, 2014 at 15:45 | comment | added | Suvrit | You're welcome! That book is great, you'll enjoy it. | |
| May 14, 2014 at 11:34 | comment | added | cs89 | Thank you very much for this precise answer and this awesome reference. I will definitely read (BCR) thoroughly. | |
| May 14, 2014 at 11:31 | vote | accept | cs89 | ||
| May 13, 2014 at 20:25 | history | answered | Suvrit | CC BY-SA 3.0 |