@AlessandroCodenotti does this make sense? $\zeta_{\Bbb R^2}:=\{\phi_S(x)\}$ that is the class of functions $\phi_S(x)=\exp(St/\ln(x))$ with generator $S:=\{S\in(\ln^2(x)):x\ne 0,1\}.$ And, $t\in\Bbb R(-\infty,\infty).$ Also, $\phi \ne 0,1.$
Def: A real Lie group is a group that is also a finite-dimensional real smooth manifold, in which the group operations of multiplication and inversion are smooth maps.
$S$ generates $\zeta.$ $t$ is a real, time parameter.
A representation of $\zeta$ gives rise to a representation of its Lie algebra.
This is the Guess-The-Number game with a twist!
Variant 1
Take any positive integer $n$.
The game-master chooses an $n$-bit integer $x$.
The player makes queries one by one, each of the form "Is $x$ (strictly) less than $k$?".
The game-master answers each query immediately, al...
Let $G$ be some locally compact group and $\mu$ its associated Haar measure. I am trying to adapt this proof that convolution on the locally compact group $(\Bbb{R},+)$ is associative. Here's what I have so far:
$$((f \ast g) \ast h)(u) = \int_{G} (f \ast g)(x)h(x^{-1}u) ~d \mu (x)$$
$$= \int_{...
On the webpage
http://tetration.org/Tetration/index.html
We are suppose to get an explaination of tetration, whatever that means exactly.
In particular I feel the pictures are not well explained.
The first two pictures show “ tetration “ and the last a “ Julia set of 2^z “.
However what is...
