conjecture 0

[tommy1729]

any convex C oo solution for f(f(x)) = exp(x)

is also an analytic solution for f(f(x)) = exp(x)

[andydude]

I suppose by "convex" you imply that the function is defined over the reals, and I suppose by "analytic" you mean real analytic. Is there an equivalent to "convex" for functions of a complex variable? Is this similar to requiring that a complex function be bounded over a strip of the complex plane?

Andrew Robbins

[tommy1729]

I suppose by "convex" you imply that the function is defined over the reals, and I suppose by "analytic" you mean real analytic. Is there an equivalent to "convex" for functions of a complex variable? Is this similar to requiring that a complex function be bounded over a strip of the complex plane?

Andrew Robbins

i do mean f(x) maps R to R yes.

though convex is more than that of course.

i assume " analytic " is false because of the fixpoint exp(x) = x ?

real analytic makes a weaker conjecture ... and more likely to be true perhaps.

as for your questions about 'convex for complex' i have no idea.


regards

tommy1729