Abstract
This chapter discusses Fourier series, Fourier transforms, and the Riemann–Lebesgue lemma. It also discusses the rapidity with which Fourier coefficients converge to zero and focuses on a unicity problem—whether Fourier coefficients determine the function. This problem is very basic in nature and is called a trigonometric moment problem. If f(x) ∈ L1(–∞, ∞) and its Fourier transform is identically zero, then f(x) = 0 almost zero.
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