We give in this chapter a compact account of Fourier analysis that we need in this book. Fuller and more rigorous treatments can be found in the books [7, 32, 33, 41].
Let f ∈ L1(Rn). Then we define the Fourier transform fˆ of f to be the function on Rn by
fˆ(ξ) = (2π)−n/2 ∫ Rn
e−ix·ξf(x) dx, ξ ∈ Rn.