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.
Rezensionen / Stimmen
"... this book is clearly written; theorems and propositions are well formulated and, if not proved, very adequate references are given." Mathematical Reviews, 2003
Auflage
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 30 mm
Gewicht
ISBN-13
978-1-86094-324-9 (9781860943249)
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Schweitzer Klassifikation
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.
