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+--- Thread: bounded derivatives and semi-group iso ( repost ?? ) (/showthread.php?tid=1710)
bounded derivatives and semi-group iso ( repost ?? ) - tommy1729 - 02/20/2023
sorry if this is a repost, im not sure.
The idea is we want for n E {0,1,2,3} , q E [0,1] and x positive real :
0 < (d/dx)^n exp^[q](x) =< (d/dx)^n exp^[q + h](x)
for any positive h such that q + h =< 1.
My fear is however this might not be analytic ?
***
edit : incorrect statement removed
***
If we relax the first equation to
The idea is we want for n E {0,1,2,3} , q E [0,1] and x positive real :
0 =< (d/dx)^n exp^[q](x) =< (d/dx)^n exp^[q+h](x)
for any positive h such that q + h =< 1.
Then I think again hoosmand equation is the solution if it even has one.
Which makes me skeptic about the first equation having analytic solutions.
so intuitive simple bounded derivatives and semi-group iso seem to have no solutions.
Nice uniqueness criterion tears.
regards
tommy1729
RE: bounded derivatives and semi-group iso ( repost ?? ) - JmsNxn - 02/21/2023
(02/20/2023, 12:56 AM)tommy1729 Wrote: 0 < (d/dx)^n exp^[q](x) =< (d/dx)^n exp^[q](x)
Sorry, Tommy. I can't understand your question because you've written \(a \le a\); when I know there's a typo somewhere in there. Could you elaborate?
Regards, James
RE: bounded derivatives and semi-group iso ( repost ?? ) - tommy1729 - 02/22/2023
(02/21/2023, 06:36 AM)JmsNxn Wrote:(02/20/2023, 12:56 AM)tommy1729 Wrote: 0 < (d/dx)^n exp^[q](x) =< (d/dx)^n exp^[q](x)
Sorry, Tommy. I can't understand your question because you've written \(a \le a\); when I know there's a typo somewhere in there. Could you elaborate?
Regards, James
Thanks for warning.
It is an unmature idea at the moment but I edited.
The idea is we want for n E {0,1,2,3} , q E [0,1] and x positive real :
0 < (d/dx)^n exp^[q](x) =< (d/dx)^n exp^[q + h](x)
for any positive h such that q + h =< 1.
regards
tommy1729
RE: bounded derivatives and semi-group iso ( repost ?? ) - tommy1729 - 02/23/2023
I changed my mind based on investigation.
optimist now.
regards
tommy1729