another question is : how many superfunctions can a function have ?

in this thread we have a lower and upper superfunction.

but when considering complex numbers and non-real fixpoints and general analytic functions , i wonder about how many superfunctions one can have and how to determine them.

note that a different branch is not considered another superfunction !

also "the inverse superfunction" is quite a weird concept , since we do not know which superfunction to invert.

thinking about this seems complicated at first , but maybe i missed something trivial.

i think this question has not been asked here before and is not easy to find in books.

correct me if im wrong.

regards

tommy1729

edit : hmm , on the other hand , following the conjecture of this thread it seems the lower and upper are in fact " the same " in some sense.

so , only 1 " true superfunction " for all entire functions afterall ?

if so then the OP must be correct in the sense that the behaviour of 1 function is also seen in the other and visa versa.

then only the behaviour of 1 function needs to be shown ... in this case (thread) might have already happened.

in this thread we have a lower and upper superfunction.

but when considering complex numbers and non-real fixpoints and general analytic functions , i wonder about how many superfunctions one can have and how to determine them.

note that a different branch is not considered another superfunction !

also "the inverse superfunction" is quite a weird concept , since we do not know which superfunction to invert.

thinking about this seems complicated at first , but maybe i missed something trivial.

i think this question has not been asked here before and is not easy to find in books.

correct me if im wrong.

regards

tommy1729

edit : hmm , on the other hand , following the conjecture of this thread it seems the lower and upper are in fact " the same " in some sense.

so , only 1 " true superfunction " for all entire functions afterall ?

if so then the OP must be correct in the sense that the behaviour of 1 function is also seen in the other and visa versa.

then only the behaviour of 1 function needs to be shown ... in this case (thread) might have already happened.