08/11/2022, 03:58 PM
Hm, I think uniqueness is exactly the problem here. If we have one real valued solution then we have a lot of real valued solutions via a real valued theta.
Maybe one can calculate some, but without having the best, its kinda futile.
Btw. this reminds me of an old question that I asked in sci.math.research about the uniqueness of the Fibonacci number extension.
Because everyone knows that \(\frac{\Phi^t-\Psi^t}{\Phi-\Psi}\) *is* an extension, but nobody knows about the *uniqueness* of this extension.
https://groups.google.com/g/sci.math.res...WX5ZriAm8I
The answer of Waldek Hebisch actually inspired me to write the article about the uniqueness of holomorphic Abel functions.
(Which then later turned out to be known by those Perturbed-Fatou-Coordinate guys.)
And here in the thread we found also another uniqueness criterion, that it is the regular iteration of the corresponding linear fractional function.
So we have a lot of uniqueness criterions for a non-real valued function, damn!
Maybe one can calculate some, but without having the best, its kinda futile.
Btw. this reminds me of an old question that I asked in sci.math.research about the uniqueness of the Fibonacci number extension.
Because everyone knows that \(\frac{\Phi^t-\Psi^t}{\Phi-\Psi}\) *is* an extension, but nobody knows about the *uniqueness* of this extension.
https://groups.google.com/g/sci.math.res...WX5ZriAm8I
The answer of Waldek Hebisch actually inspired me to write the article about the uniqueness of holomorphic Abel functions.
(Which then later turned out to be known by those Perturbed-Fatou-Coordinate guys.)
And here in the thread we found also another uniqueness criterion, that it is the regular iteration of the corresponding linear fractional function.
So we have a lot of uniqueness criterions for a non-real valued function, damn!