Re: Fractional Transforms
- From: amy666 <tommy1729@xxxxxxxxxxx>
- Date: Mon, 15 Dec 2008 16:31:59 EST
Robert wrote :
David C. Ullrich <dullrich@xxxxxxxxxxx> writes:
A few days ago I decided there was no point,considering the audience,
in pointing out that the existence of a T with L =T^2 is clearly
impossible if we interpret things very strictly. Wehave
L: X -> Y where X and Y are very different spacesof functions.
If T were a functional square root of L then we'dneed to have
somehow T:X -> Z and also T:Z -> Y; if we take T tohave
a well-defined domain and co-domain then it followsthat
X = Y. Of course this doesn't quite rule out theexistence
of some kernel that does the job at least formally.
On the other hand there are spaces X such that L: X
-> X.
For example, let X be the space of continuous
functions f on (0,infty)
such that x^(1/2) f(x) is bounded.
--
Robert Israel
israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics
http://www.math.ubc.ca/~israel
University of British Columbia Vancouver,
BC, Canada
thus Fractional Transform exist for the space of continuous functions f on (0,infty) such that x^(1/2) f(x) is bounded ?
regards
tommy1729
.
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