03/19/2021, 06:55 AM
James,
Thanks for noticing the use of matrices. In learning how to write math papers my understanding is first you built up a series of simple papers and only then did you explain your grand overarching view. While this might work for a series of papers written in a decade, it doesn't work for half a century.
My approach was to prove the complex numbers example for \( a \) and \( b \) but to have the proof valid for the general linear group.
\(
a,b \in \mathbb{GL}(n) \\
k \in \mathbb{N}\\
a \rightarrow b \rightarrow k \)
Transfer functions
The functional equations of Abel and Schroeder are derived in my work along with their specific properties. For example Abel's equation only works when \( f'(z)=1 \).
Thanks for noticing the use of matrices. In learning how to write math papers my understanding is first you built up a series of simple papers and only then did you explain your grand overarching view. While this might work for a series of papers written in a decade, it doesn't work for half a century.
My approach was to prove the complex numbers example for \( a \) and \( b \) but to have the proof valid for the general linear group.
\(
a,b \in \mathbb{GL}(n) \\
k \in \mathbb{N}\\
a \rightarrow b \rightarrow k \)
Transfer functions
The functional equations of Abel and Schroeder are derived in my work along with their specific properties. For example Abel's equation only works when \( f'(z)=1 \).
Daniel