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Topic: Is it possible to bound these functions?
Replies: 3   Last Post: Apr 5, 2013 10:15 PM

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William Elliot

Posts: 1,703
Registered: 1/8/12
Re: Is it possible to bound these functions?
Posted: Apr 5, 2013 5:00 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I've not the time to decipher the TeX.
Would you restate the problem simply, with plain text?

On Thu, 4 Apr 2013, Brad Cooper wrote:

> Define A{f(x)} as a mapping from the set of functions defined on the interval [0,1] to the Reals.
>
> The functions are as "nice, smooth and integrable" as you may want them to be.
>
> begin{equation*}
> A{f(x)} = {left[int_0^1 cosleft(int_0^x f(t)dtright) dxright]}^2 +
> {left[int_0^1 sinleft(int_0^x f(t)dtright) dxright]}^2
> end{equation*}
>
> Given that a leq f(x) leq b, can it be shown that A{a} geq A{f(x)} geq

A{b} ?
>
> Cheers,
> Brad
>
> PS Sorry about using LaTeX code. Is there a better way to show equations in Google Groups?
>




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