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




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



