03/03/2023, 01:09 PM
hello guys
You seem to be missing the fact that this IS EQUAL TO THE SEMI-GROUP ISOM I have been talking about for months.
This thing is a uniqueness criterion !
Also real-differentiable may not be equal to complex differentiable.
And in older posts I already called something flow theory which somewhat relates.
But yeah , analytic over the rationals implies real-analytic over the reals for smooth functions.
If you can show the function as smooth over the complex and analytic over the gaussian or eisenstein rationals then it is analytic.
This is just good old basic analysis.
The 2sinh has this property by the fact of its fixpoint at 0.
the compositions of iterations of 2sinh with ln and exp are just conjugate compositions , so the property carries over from the 2sinh super to the super of the 2sinh method.
It is known to be C^oo so it is smooth over the rationals.
Question is if it is analytic.
Im unaware of nontrivial cases where semi-group iso that is not analytic.
I posted conjectures about these in the past.
regards
tommy1729
You seem to be missing the fact that this IS EQUAL TO THE SEMI-GROUP ISOM I have been talking about for months.
This thing is a uniqueness criterion !
Also real-differentiable may not be equal to complex differentiable.
And in older posts I already called something flow theory which somewhat relates.
But yeah , analytic over the rationals implies real-analytic over the reals for smooth functions.
If you can show the function as smooth over the complex and analytic over the gaussian or eisenstein rationals then it is analytic.
This is just good old basic analysis.
The 2sinh has this property by the fact of its fixpoint at 0.
the compositions of iterations of 2sinh with ln and exp are just conjugate compositions , so the property carries over from the 2sinh super to the super of the 2sinh method.
It is known to be C^oo so it is smooth over the rationals.
Question is if it is analytic.
Im unaware of nontrivial cases where semi-group iso that is not analytic.
I posted conjectures about these in the past.
regards
tommy1729