05/27/2016, 04:03 AM

Hey Mphlee. I corrected some of the mistakes I made on my old arxiv page. They were rather small (the same result holds), the new version is also being edited by my professor, and just some double checking being done by him.

And to your question on the super function operator, I have added a little bit about this.

If is a set in which all its elements are holomorphic for , take the real positive line to itself, have a fix point such that and for all

then..

There is a semi group of operators such that acts on . Where more beneficially, the semi group is isomorphic to

This semi group being for where

and if

then

I have no idea to be honest. This is where I'm looking. The analysis is extensively simplified using ramanujan's master theorem. and some key points arise. I have a few well thought out points but nothing too expansive.

is injective in and (where is the imaginary period in .

The operator is injective as well on the function space as defined above.

The only fixed point of I can think of are constant functions. Since

and if then surely

It always follows that though. This is exemplified by

And to your question on the super function operator, I have added a little bit about this.

If is a set in which all its elements are holomorphic for , take the real positive line to itself, have a fix point such that and for all

then..

There is a semi group of operators such that acts on . Where more beneficially, the semi group is isomorphic to

This semi group being for where

and if

then

(05/23/2016, 07:25 PM)MphLee Wrote: I would like to ask you: have you some ideas/intuition on the behavior of this map and its dynamics in general?

I have no idea to be honest. This is where I'm looking. The analysis is extensively simplified using ramanujan's master theorem. and some key points arise. I have a few well thought out points but nothing too expansive.

Quote: Is it injective?

is injective in and (where is the imaginary period in .

The operator is injective as well on the function space as defined above.

Quote:Has it fixed points?

The only fixed point of I can think of are constant functions. Since

and if then surely

It always follows that though. This is exemplified by