It might be important to rewrite min since min is crucial in fake function theory.
Sheldon is correct ofcourse ; min f(x) = f(w) , f ' (w) = 0.
But the inverse of f ' can be complicated.
So the idea here is to estimate min with other tools.
For instance
G (f) = f/(f+1)
T = growth f
Min f ~ integral_1^oo 1/f dx
Or more advanced
Min f(x)/x^n ~ lim m -> oo q(m)
Where
Q(m) = exp^[m+T]( integral_1^(n m) ln^[m+T](G ( f(x)/x^n )) dx / (n m) ).
There are probably better ones.
But that is the idea.
For proofs that may be important.
Maybe there is An argument principle equivalent ... But im concerned about the nonreal w messing up.
Regards
Tommy1729
Sheldon is correct ofcourse ; min f(x) = f(w) , f ' (w) = 0.
But the inverse of f ' can be complicated.
So the idea here is to estimate min with other tools.
For instance
G (f) = f/(f+1)
T = growth f
Min f ~ integral_1^oo 1/f dx
Or more advanced
Min f(x)/x^n ~ lim m -> oo q(m)
Where
Q(m) = exp^[m+T]( integral_1^(n m) ln^[m+T](G ( f(x)/x^n )) dx / (n m) ).
There are probably better ones.
But that is the idea.
For proofs that may be important.
Maybe there is An argument principle equivalent ... But im concerned about the nonreal w messing up.
Regards
Tommy1729
