Timeline for Are there projective version of real Positivstellensatz?
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| Oct 28, 2010 at 16:24 | comment | added | Noah Stein | (I will stop using $t$ lest I get confusing.) Basically Stengle's condition is $sf = 1 + SOS$, whereas I wrote $sf = \sum_i x_i^{2k} + SOS$. It seems to me that $\sum_i x_i^{2k}$ is a reasonable homogeneous analog of Stengle's $1$: a term which makes strict positivity evident. I would imagine one could also use something like $(\sum_i x_i^2)^k + SOS$ to be a little more natural,. I somehow feel like I'm missing the point. Could you give an example of a certificate for homogeneous polynomials which would look more natural to you (whether it works or not)? Or was that the question? | |
| Oct 28, 2010 at 15:10 | comment | added | user2529 | This is sort of against the spirit of Positivstellensatz in that we cannot see from the form the equation $sf=t$ that $f$ is strictly positive. You put conditions on $t$. | |
| Oct 28, 2010 at 15:01 | history | answered | Noah Stein | CC BY-SA 2.5 |