Re: Fractional Transforms

On Tue, 16 Dec 2008 16:20:10 +1100, "rancid moth"
<rancidmoth@xxxxxxxxx> wrote:


"David C. Ullrich" <dullrich@xxxxxxxxxxx> wrote in message
news:amgdk4h906qlra8m60tgiqisbn5nkgs7ka@xxxxxxxxxx
On Mon, 15 Dec 2008 14:05:57 -0600, Robert Israel
<israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> 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. We have
L: X -> Y where X and Y are very different spaces of functions.
If T were a functional square root of L then we'd need to have
somehow T:X -> Z and also T:Z -> Y; if we take T to have
a well-defined domain and co-domain then it follows that
X = Y. Of course this doesn't quite rule out the existence
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.

Heh, very good - I considered the possibility of such an X existing
but didn't think of this simple example.

(Readers who are wondering why this X has that property
should contemplate the Laplace transform of 1/t^(1/2)...)
[cut]

Yes. i was wondering about that.

Also - what do you mean "..there was no point, considering the audience..."

I said there _was_ no point, referring to a time in the past
when you were not part of the audience.

I know i'm a little wayward with my mathematics, but generally i'm ok and
get there in the end...or at least i thought i was ok.

At the very least i thought i was polite enough to post and get responses.
perhaps not.

??? You _got_ a response. From me.

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.

Relevant Pages

  • Re: Fractional Transforms
    ... X = Y. Of course this doesn't quite rule out the existence ... "Understanding Godel isn't about following his formal proof. ... Thanks for the response - from both you and Robert. ...
    (sci.math)
  • Re: Fractional Transforms
    ... impossible if we interpret things very strictly. ... X = Y. Of course this doesn't quite rule out the existence ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... >> existence of a proof in T of P, ... The importance of it being a ... >> formal proof is that it can be algorithmically verified, ... addressing whether or not AC is "true" in some other sense. ...
    (comp.theory)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... >> existence of a proof in T of P, ... The importance of it being a ... >> formal proof is that it can be algorithmically verified, ... addressing whether or not AC is "true" in some other sense. ...
    (sci.math)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... >> existence of a proof in T of P, ... The importance of it being a ... >> formal proof is that it can be algorithmically verified, ... addressing whether or not AC is "true" in some other sense. ...
    (sci.logic)