02/18/2009, 12:32 AM
any convex C oo solution for f(f(x)) = exp(x)
is also an analytic solution for f(f(x)) = exp(x)
is also an analytic solution for f(f(x)) = exp(x)
conjecture 0

02/18/2009, 12:32 AM
any convex C oo solution for f(f(x)) = exp(x)
is also an analytic solution for f(f(x)) = exp(x)
02/18/2009, 05:23 AM
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
02/18/2009, 04:14 PM
andydude Wrote: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? 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 
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