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“Characteristic Functions” as a book category covers works centered on two closely related mathematical notions: (1) the characteristic (indicator) function of a set, fundamental in measure theory, integration, and optimization/convex analysis; and (2) the characteristic function of a random variable, i.e., the Fourier transform of a probability distribution, a core tool in probability and statistics. Books in this category range from textbooks and monographs on the theory—covering properties, inversion and continuity theorems, limit theorems (e.g., central limit theorem), stable laws, infinite divisibility, Lévy–Khintchine representations, and Lévy processes—to applied and computational treatments, including empirical characteristic function methods, numerical inversion, and applications in signal processing, econometrics/finance, physics, and machine learning. The category may also include problem collections and reference works that develop the necessary Fourier/harmonic analysis background and illustrate how indicator functions and distributional characteristic functions unify ideas across analysis, probability, and data science.

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