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

Farkas, Walter; Jacob, Niels; Schilling, René L. (2001): Feller semigroups, Lp-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols. In: Forum Mathematicum, Vol. 13, No. 1: pp. 51-90

Abstract

The question of extending L-p-sub-Markovian semigroups to the spaces L-q, q > P, and the interpolation of LP-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 role 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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0933-7741
• Alliance/National Licence: This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
• Language: English