In this volume two topics are discussed: the construction of Feller and Lp–sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp –sub-Markovian semigroups in their associated Bessel potential spaces, Stein's Littlewood–Paley theory, global properties of Lp–sub-Markovian semigroups, and estimates for transition functions.

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...this book is clearly written; theorems and propositions are well formulated... -- Mathematical Reviews, 2003

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