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Azupol123
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Homework Statement
Let g: R→R be an infinitely differentiable function satisfying g(x)=0[itex]\forall[/itex] |x|>1
Consider the integral I[itex]\lambda[/itex] = ∫g(x)sin([itex]\lambda[/itex]x2) dx taken from -∞ to +∞
Prove that I[itex]\lambda[/itex]→0 and identify the rate of decay as [itex]\lambda[/itex]→0
I have no idea how to start this. I thought maybe differentiation under the integral or using Bessel's inequality?