Pseudo Differential Operators And Markov Processes, Volume Ii: Generators And Their Potential Theory
Imperial College Press (Verlag)
9781860943249 (ISBN)
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.
Generators 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.
| Verlagsort | London |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-13 | 9781860943249 / 9781860943249 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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