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From: fulk@sunybcs.UUCP (Mark Fulk)
Newsgroups: net.math
Subject: Re: infinite differentiability
Message-ID: <854@sunybcs.UUCP>
Date: Wed, 14-Dec-83 09:45:57 EST
Article-I.D.: sunybcs.854
Posted: Wed Dec 14 09:45:57 1983
Date-Received: Sat, 17-Dec-83 07:36:22 EST
References: <6784@arizona.UUCP>
Organization: SUNY/Buffalo Computer Science
Lines: 13

To prove exp(D) f = f, you need more than differentiability OR even
C infinity; you need that f is analytic.  A good example:
f(x) = exp(-1/x*x) if x>0; f(x) = 0 otherwise.  Taking x in the
statement of the problem to be 0, we would have:

(exp(D) f)(0) = 0 != f(1) = 1/e.

This is, of course, a standard example from advanced calculus.
-- 
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