Abstract
This chapter discusses some properties of characteristic functions. It also discusses some problems concerning Fourier coefficients or Fourier transforms. A sequence of functions over (—∞, ∞) is said to converge locally uniformly if it converges uniformly in every finite interval. In this case, the limit is called the locally uniform limit. If a function is nonnegative definite, then it means that it is so in (—∞, ∞). A continuous function f(t) with f(0) = 1 is a characteristic function if and only if it is nonnegative definite. The chapter also discusses the functions of the Wiener class.
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