Appendix B: Fourier analysis
This section contains a brief account of the facts from classical Fourier analysis and their consequences that are used at various points above.
Suppose that f (x) is a (real or) complex-valued function that is absolutely integrable:
The Fourier transform is defined by
The condition (B.0.1) implies that is bounded and continuous. It can also be shown that (x) → 0 as |x| → ∞, so is uniformly ...