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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: 2,637 Registered: 1/8/12
Re: Is it possible to bound these functions?
Posted: Apr 5, 2013 5:00 AM

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,
>
> PS Sorry about using LaTeX code. Is there a better way to show equations in Google Groups?
>

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