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After recalling essentials of analysis -- including functional analysis, convexity, distribution theory and interpolation theory -- this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students.
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Pseudo-differential operators and Markov processes, Niels Jacob
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- 1996
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