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Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: | fg | <= 1/2 ( f*f + g*g ) ???
Replies: 6   Last Post: Feb 17, 2011 12:31 PM

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sto

Posts: 82
Registered: 3/27/08
| fg | <= 1/2 ( f*f + g*g ) ???
Posted: Feb 16, 2011 9:28 PM
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Let (X,m) me a measure space and f,g be in L2(X,m)

Presumably it is obvious that for every x in X,

|f(x)g(x)| <= 1/2 ( f(x)*f(x) + g(x)*g(x) )

How do you prove this rigorously? I've tried looking at the RHS as the
area of a rectangle, I've tried the formula for the long side of an
obtuse triangle, I've tried looking at the diagonals of a parallelogram
and nothing works.
Thanks,
-sto

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