06/10/2021, 12:21 PM
Hi, I know this is not directly related to tetration. It is related to iteration theory and solving functional equations.
https://math.stackexchange.com/questions...alpha-beta
The question is the following \( f(g,\beta\alpha,x+y)=f(g^\alpha,\beta,x)f(g,\alpha,y)
\)
Mind that here x,y can be thought to be numbers. But the crucial part is that \( \alpha \), \( \beta \) and \( g \) are intended to be matrices, formal powerseries or functions (non commutative objects in general) under composition.
I ask also here because with JmsNxn deep familiarity with iterated composition (in the question i rendered the Omega notation as a product to not scare away normies) I could get some knowledge.
https://math.stackexchange.com/questions...alpha-beta
The question is the following \( f(g,\beta\alpha,x+y)=f(g^\alpha,\beta,x)f(g,\alpha,y)
\)
Mind that here x,y can be thought to be numbers. But the crucial part is that \( \alpha \), \( \beta \) and \( g \) are intended to be matrices, formal powerseries or functions (non commutative objects in general) under composition.
I ask also here because with JmsNxn deep familiarity with iterated composition (in the question i rendered the Omega notation as a product to not scare away normies) I could get some knowledge.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
