Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / 4 / i

First take

f, g \in L^{1} (R)

s = x + y

h (k) = \int_{R} \int_{R} e^{- ik x} \overline{f (y)} g (x + y) d y d x = [\int_{R} \overline{f (y)} e^{ik y} d y] [\int_{R} g (s) e^{- ik s} d s] = \overline{f (k)} g (k) .

x + y

are both essential to this convention.

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