Generators and their potential theory
著者
書誌事項
Generators and their potential theory
（Pseudo differential operators and Markov processes / Niels Jacob, v. 2）
Imperial College Press, c2002
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注記
Bibliography: p. [417]-441
Includes indexes
内容説明・目次
内容説明
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.
目次
- 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.
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