(11/07/2012, 08:23 PM)JmsNxn Wrote: I've been doing a lot of research in areas around linear operators and I've found the following theorem. If it's useful I'll prove how I got it. If not I won't.
We can express the following:
And so therefore we can write:
If you can't noticeis a linear operator; so:
This result is quite elaborate to prove and requires knowledge of Hilbert spaces. I just found this expression recently of a more general result that I am more interested in. We must remember this is right hand composition.
Nonetheless; is it easier to iterate a linear operator than how we usually do it? I can apply these methods for pentation and every hyper operator; formally; without considering convergence of the integrals. I'm still in the baby steps.
Questions, comments?
I can do everything I just did for iteration of any base as well. Not sure about convergence though. We can actually turn every super-function into iteration of a linear transformation. However; again; formally; not sure about convergence. I'm working on a paper that proves all of this but feedback helps; maybe someone's seen this.
Edit: What's cool about this is we do not require a fixpoint!
Interesting. Could you give a few more details about how you got it -- e.g. what other theorems did you use, etc.?
I just posted a question to mathoverflow here:
http://mathoverflow.net/questions/111752...-transform
(EDIT: I Deleted this -- see NEW POST)