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meromorphic idea

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meromorphic idea
andydude Offline
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05/13/2009, 09:51 PM (This post was last modified: 05/13/2009, 09:55 PM by andydude.)
(05/13/2009, 04:52 PM)tommy1729 Wrote: are there meromorphic functions f(x) so that they commute with exp(x) ?

I'm not sure if this is important, but I think what is important is whether or not:

"For all f(x) that satisfy \( f(\exp(x)) = \exp(f(x)) \), there exists a unique real number t such that \( f(x) = \exp^t(x) \)."

I'm not convinced that this is always true for holomorphic/meromorphic functions. I'm sure its false for for arbitrary (or piecewise-defined) functions. I also think this would be useful in characterizing fractional iterates.

Andrew Robbins
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Messages In This Thread
meromorphic idea - by tommy1729 - 05/13/2009, 04:52 PM
RE: meromorphic idea - by andydude - 05/13/2009, 09:51 PM
RE: meromorphic idea - by tommy1729 - 05/13/2009, 11:18 PM

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