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May 23

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Help for an estimate

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Hello, I would like to estimate several derivatives wrt the variable s of the integral function

I am looking for estimates of the form

where C does not depend on a. In principle one could estimate every single derivative but it would take a very long time and so I am looking for a general scheme.

Any idea?--Pokipsy76 (talk) 16:34, 23 May 2010 (UTC)[reply]

As a firs step, I'd change variable and write Not clear what's the range of a and s, btw.--pma 17:06, 23 May 2010 (UTC)[reply]
Thank you for your help. Your suggestion is very smart (I don't think I could ever think it) indeed the integral becomes
so when I derive it wrt s I obtain a simple algebraic expression which can be estimated easily. It was not obvious to me that having the variable only on the integration domain would allow to eliminate the integral after a derivative.--Pokipsy76 (talk) 17:38, 23 May 2010 (UTC)[reply]

Isometries of the Poincare Disc

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Hi everyone,

Could anyone direct me to a proof of the fact that orientation-preserving isometries of the hyperbolic disc are of the form

where and ?

I have the result but I can't seem to find a proof anywhere online. Of course, if you could provide a short proof instead that would be greatly useful too, but I'm very much capable of understanding a proof on my own if it'll save you time linking be to one rather than writing it out yourself :-)

Thanks very much,

82.133.94.184 (talk) 23:05, 23 May 2010 (UTC)[reply]

The characterization of the holomorphic automorphisms of the disk is in almost every book on complex variable, e.g Rudin's Real and complex analysis. Here there is something in Möbius transformation. --pma 04:12, 24 May 2010 (UTC)[reply]