Description
Book SynopsisIn 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.
Trade Review"... this book is clearly written; theorems and propositions are well formulated and, if not proved, very adequate references are given." Mathematical Reviews, 2003
Table of ContentsGenerators of Feller and sub-Markovian semigroups: second order elliptic differential operators; some second order hypoelliptic differential operators; pseudo-differential operators with negative definite symbols; Hoh's symbolic calculus; estimates for operators; constructing Feller and sub-Markovian semigroups; further analytic approaches; perturbation results; subordinate semigroups; operators of variable order of differentiation. Potential theory: capacities; abstract Bessel potential spaces; function spaces associated with continuous negative definite functions; sub-Markovian semigroups in their Bessel potential spaces; Stein's Littlewood-Paley theory; invariant sets, recurrence and transience; kernel representations and estimates for kernels; Nash-type inequalities and their consequences.
