Iteration with two analytic fixed points

[tommy1729]

you got the fixpoints derivatives connection right. 

but how do you know both regulars agree ?

They don't, I made a short sketch why it can not in this particular case (or generally for entire functions) from the paper of Karlin&McGregor
just some post ago

yes but that limit is the whole neigbourhood of the second fixpoint.

I mean analytic from say the open interval between 0 and 1.

So when fixpoint 0 and 1 are given 

analytic around x belonging to

]0,1[

Im sorry im responsable for some errors miscommunications etc.

I lack time and the ideas are coming fast.

***

Then again hmm

if the regular must be analytic in 0 when taking regular in 0 and similar to the point 1 ...

then I guess we have 

analytic in 

[0,1[ when expanded in 0.

and

]0,1] when expanded in 1.

and the issue is not analytic continuation.

So that seems like 2 different superfunctions yeah....


maybe

***

I was thinking about fusing the two methods.

But then they are not regular anymore so we loose the semi-group homom probably.

hmmm

***

im thinking ...


Thanks for your efforts anyway.



regards

tommy1729