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twice a superfunction
#2
(08/11/2010, 04:28 PM)tommy1729 Wrote: i have been thinking about the following often :

how and when is a function a 'superfunction for two functions' and what degrees of freedom do we have ?

for instance

assume the following equation

f(x+1) = A(f(x))
f(x+i) = B(f(x))

and A and B are somewhat related : they commute of course and satisfy some equation ( e.g. A = sin(log(B)) )

i assume there is no freedom for f(z) apart from choosing f(0).

( once again , riemann mapping theorem and double periodic functions convinced me of that )

but its not so clear when we have a solution and when not.

also , could this be a usefull uniqueness criterion ?

its seems we need at least 3 criterions for a solution to exist :

1) A and B commute
2) A and B share the same fixpoints
3) its clear the superfunction of A and B is nonparadoxal at complex oo.

maybe 4 : 4) the superfunction becomes periodic or semi-periodic near complex oo. ( although that might follow from 3 )

regards

tommy1729


and


but this doesn't mean that should hold always?

MathStackExchange account:MphLee
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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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