Semigroups Defined by Additive Processes


Lieven Smits and Johannes A. van Casteren (here are some of his many works)

Bibliographical Reference

This paper was presented by the authors at the Second International Conference on Semigroup Theory and Evolution Equations, in the Dutch town of Delft.

The conference proceedings have appeared as volume 135 in the series "Lecture Notes in Pure and Applied Mathematics" by Marcel Dekker Inc., New York 1991, ISBN 0-8247-8545-2. The title is "Semigroup Theory and Evolution Equations," edited by Philippe Clément, Enzo Mitidieri and Ben de Pagter. The current paper is on pages 463-482 of the book.


We study semigroups, or more general evolution families of operators on a Banach space of functions. The classical probabilistic view on such operators uses additive functionals of the Markov sample space. We show that some of the most imporant classical results on domains an integral kernels can be salvaged if the usual hypothesis on bounded variation is dropped. This is a necessary generalization if the theory must be applied to the magnetic case, because the Itô integrals involved do not have bounded variation.


The authors hold only a single copy of the book each, therefore please consult your librarian and/or local academic bookstore.


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  25. Voigt, J., Lecture at the 2nd International Conference on Trends in Semigroup Theory and Evolution Equations, Delft, 25/9-29/9/1989: Schrödinger Operators with Singular Potentials.

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