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-   -   Positive polynomial in two real variables (http://www.physicsforums.com/showthread.php?t=40683)

 gvk Aug26-04 03:55 PM

Positive polynomial in two real variables

Does every positive polynomial in two real variables attain its lower bound in the plane? :yuck:

 Hurkyl Aug26-04 06:54 PM

Let's start by investigating how it could fail.

Do you know of any way that a continuous function can fail to attain its lower bound?

 gvk Aug27-04 07:27 AM

Quote:
 Quote by Hurkyl Let's start by investigating how it could fail. Do you know of any way that a continuous function can fail to attain its lower bound?
Do you mean the function which asymptoticaly aproaches the plane when x ->infinity?
It seems to me that, according the Sylvester's theorem the positive defined polynomial never reaches the plane, and it does not matter how behave the continuous function.

 Hurkyl Aug27-04 05:46 PM

I was suggesting a possible line of attack: examime what properties a continuous function must have if it doesn't attain its lower bound, then prove a polynomial can't have those polynomials.

But it sounds like you already have a line of attack... how are you proposing to use Sylvester's theorem?

(I don't recall the theorem; a quick google search doesn't provide anything that seems relevant)

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