Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Generalized Kneser superfunction trick (the iterated limit definition)
It's back to the drawing board! So I thought I'd post how close I came in the third iteration of this paper.


Note in this space that the transfer operator exists. Then there exists a super function operator on , call it ,

And if

There exists a in which,

BUT I CAN'T GET . I think this might be off base even trying to prove it with this much information. So I nearly have a set which has a conjugate property, but this pesky condition at negative infinity has me stumped. Largely because the behaviour at positive infinity is used to construct and consequently it encodes nothing about the behaviour at negative infinity. Damn it, so close!

As I said, back to the drawing board trying to find a set of functions which satisfies the conjugate property. I was so close, too!

Regards, James
Honestly, at this point in my evaluation of my ideas (my approach), I don't think constructing a monoid globally on is hopeful. I definitely got ahead of myself in thinking I could get a monoid . I think, doing this in a local setting is easier--and far more probable. Even if we focus on the trivial case. That would be when we can just multiply our Schroder functions. By this I mean, if and and are holomorphic in a neighborhood of and , then,

Is holomorphic in a neighborhood of zero. Here,

And this is of course a group under composition; in which belongs if ... I think this may be a more tractable approach to constructing a general categorical theory.  This set of sheaves do satisfy the conjugate property. But it's a little useless globally (it just means there's a taylor series in a neighborhood of zero). I do think its doable in the global sense, but probably in a local setting, is the correct way to approach the larger theory of conjugation. I definitely can't show it on the real line, but I may be able to do it locally in the complex plane (not necessarily about a fixed point). I'll have to entirely alter my approach though.

Nonetheless the group, under composition, of sheaves ,

Is a very good place to start. Of which the conjugate property is almost satisfied here. And furthermore, this is a GROUP which almost satisfies the conjugate property. We'd just have to allow for and somehow massage this case to allow for the conjugate property--while still staying in the group.

I forgot how useless I am at deep questions in real-analysis, so I'll stick to holomorphy. I'm so angry I can't get it on the real-line ):<

Regards, James

Possibly Related Threads...
Thread Author Replies Views Last Post
  Some "Theorem" on the generalized superfunction Leo.W 21 649 05/11/2021, 08:41 PM
Last Post: MphLee
  Alternative manners of expressing Kneser JmsNxn 1 296 03/19/2021, 01:02 AM
Last Post: JmsNxn
  Questions about Kneser... JmsNxn 2 494 02/16/2021, 12:46 AM
Last Post: JmsNxn
  Generalized phi(s,a,b,c) tommy1729 6 829 02/08/2021, 12:30 AM
Last Post: JmsNxn
  Kneser method question tommy1729 9 7,518 02/11/2020, 01:26 AM
Last Post: sheldonison
  iterated derivation Xorter 0 1,612 06/09/2019, 09:43 PM
Last Post: Xorter
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 3,303 03/03/2019, 08:55 AM
Last Post: Chenjesu
  1st iterated derivatives and the tetration of 0 Xorter 0 2,415 05/12/2018, 12:34 PM
Last Post: Xorter
  Iterated nand Xorter 2 5,877 03/27/2017, 06:51 PM
Last Post: Xorter
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 24,981 08/22/2016, 12:19 AM
Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)