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 twice a superfunction tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 03/26/2014, 01:23 PM Considering the thread http://math.eretrandre.org/tetrationforu...hp?tid=844 It seems to follow that from the (probably) fact that sexp is not pseudounivalent then a superfunction cannot be twice a superfunction on a half-plane. The proof sketch is as follows : Let f be a nonspeudounivalent superfunction. Lef f(a)= b. Then there must exist for most such a and b : f(a2)=f(a3)=f(a)=b where a2 and a3 are lineair indep. (real lineair indep of course ) then from the 2 functional equations that make up twice the superfunction it follows that f must be double periodic. ( the superfunctions equations are in the directions a-a2 and a-a3 ) Since double periodic functions are not entire , then the superfunction cannot be analytic on a halfplane. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread twice a superfunction - by tommy1729 - 08/11/2010, 04:28 PM RE: twice a superfunction - by MphLee - 03/24/2014, 09:12 PM RE: twice a superfunction - by tommy1729 - 03/25/2014, 12:34 AM RE: twice a superfunction - by MphLee - 03/25/2014, 08:51 AM RE: twice a superfunction - by tommy1729 - 03/26/2014, 01:23 PM RE: twice a superfunction - by MphLee - 03/26/2014, 03:34 PM

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