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Published online by Cambridge University Press: 27 July 2019
Chapter 3 studies semigroups on function spaces obtained via convolution semigroups of probability measures. Motivating examples that are studied in detail are the heat kernel (Brownian motion) and the Poisson kernel (Cauchy process). The characteristic functional (Fourier transform) is used to establish the Levy–Khinchine formula, and applications are given to stable laws. The generator and the semigroup are written as pseudo-differential operators.
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