Feller semigroups, Lp-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols

Walter Farkas; Niels Jacob; René L. Schilling

doi:10.1515/FORM.2001.51

Article

Feller semigroups, L^p-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols

Walter Farkas , Niels Jacob and René L. Schilling

Published/Copyright: March 4, 2009

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From the journal Volume 13 Issue 1

Abstract

The question of extending L^p-sub-Markovian semigroups to the spaces L^q, q > p, and the interpolation of L^p-sub-Markovian semigroups with Feller semigroups is investigated. The structure of generators of L^p-sub-Markovian semigroups is studied. Subordination in the sense of Bochner is used to discuss the construction of refinements of L^p-sub-Markovian semigroups. The rôle played by some function spaces which are domains of definition for L^p-generators is pointed out. The problem of regularising powers of generators as well as some perturbation results are discussed.

Received: 1999-06-21

Accepted: 2000-04-10

Published Online: 2009-03-04

Published in Print: 2001-January

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https://doi.org/10.1515/FORM.2001.51