05/05/2021, 02:59 AM
Hey, Leo
Welcome to the forum! It's always nice to get fresh blood.
This is interesting; I'm quite the fan of the notation \( \zeta(f|h) h = f\zeta(f|h) \).
I'm wondering, do you have any general idea on how to define the character,
\(
\zeta(f|h)
\)
For general instances? This is something I've been stuck on; developing a general theory to handle arbitrary \( f,h \); and I keep hitting dead-ends. I know MphLEE is a fan of black boxing it. I'm curious to hear what he'll have to say about this. As to conjugating fixed points, this is pretty standard, and many authors have done that before. The trouble is doing it for exotic scenarios, and not just when it's convenient. I do believe that generally finding well behaved solutions to,
\(
f\phi = \phi g\\
\)
Is an open problem. And really, the famous examples are the Schroder/Abel/Bottchner equations. Doing this, for say \( \phi = \zeta(tan(z) | \exp(\exp(z))) \) would be something else though, lol.
Anyway, welcome to the forum! I hope we can be of service, and we can all learn together.
Regards, James
Welcome to the forum! It's always nice to get fresh blood.
This is interesting; I'm quite the fan of the notation \( \zeta(f|h) h = f\zeta(f|h) \).
I'm wondering, do you have any general idea on how to define the character,
\(
\zeta(f|h)
\)
For general instances? This is something I've been stuck on; developing a general theory to handle arbitrary \( f,h \); and I keep hitting dead-ends. I know MphLEE is a fan of black boxing it. I'm curious to hear what he'll have to say about this. As to conjugating fixed points, this is pretty standard, and many authors have done that before. The trouble is doing it for exotic scenarios, and not just when it's convenient. I do believe that generally finding well behaved solutions to,
\(
f\phi = \phi g\\
\)
Is an open problem. And really, the famous examples are the Schroder/Abel/Bottchner equations. Doing this, for say \( \phi = \zeta(tan(z) | \exp(\exp(z))) \) would be something else though, lol.
Anyway, welcome to the forum! I hope we can be of service, and we can all learn together.
Regards, James