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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