(03/31/2015, 08:50 PM)JmsNxn Wrote: The goal is to do it in a much more general setting. I am working very hard on cleaning it up and making sure all the proofs pop out like clock work from the more general schema.I can't really follow some of the step but I think I got what your going for. The complex analysis that youre using is really crazy for me atm.
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I'm just trying to rigorize everything now. The skeleton is there, I just need to prop it up with some muscular rigor.
Anyways I always believed that one of the ways to reach the solution was inside operator theory (aka application of the analysis to higher order functions).
Quote:\( \mathcal{C}_\phi \) is a contraction operator, this proves invaluable to the generalization.
About the contraction operator, the concept is new for me (Operator theory is still new for me) but maybe I'm missing something...Did you present a normed space of functions in your paper? Because the contraction op. need the operator norm in order to be defined, and operator norm is defined using the norm(s) of the space(s) (if I recall correctly it is the operator norm is the smallest number that bounds the operator on its domain). Wich norm is used usually in these kind of frameworks? (sorry if the question is stupid).
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
