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Science Forum Index » Mathematics Forum » amplitude set
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| dumb_founded |
 Posted: Tue Feb 22, 2005 8:58 am |
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let there be a set of functions such that the amplitude of the
functions over each point in an interval equals some nonnegative
function over that interval. So, for y member set, we have that
abs[y(s)]=g(s), g nonnegative. Why would this set be nonconvex? |
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| Stuart M Newberger |
| Posted: Tue Feb 22, 2005 6:28 pm |
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dumb_founded wrote:
Quote: let there be a set of functions such that the amplitude of the
functions over each point in an interval equals some nonnegative
function over that interval. So, for y a member of the set, we have
that
abs[y(s)]=g(s), g nonnegative. Why would this set be nonconvex?
Say real valued functions and at least 2 functions not identical on
your interval ,then at some s,one function has value g(s)=A>0 and the
other -A so the amplitudes are both A.Then the average of the two
functions ( particular convex combination) is 0 at s so the set is not
convex since o|=g(s).If your functions are complex valued I guess you
work a little bit harder with the same idea.Regards,Stuart M Newberger. |
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