Full paper in PDF format:
$%A. Potrykus, A symbolic calculus and a parametrix construction for pseudodifferential operators with non-smooth negative definite symbols, Rev. Mat. Complut. 22 (2009), no. 1, 187–207.%$

A Symbolic Calculus and a Parametrix Construction for Pseudodifferential Operators with Non-Smooth Negative Definite Symbols
Alexander POTRYKUS
Department of Mathematics
Swansea University
Singleton Park, Swansea
SA2 8PP — United Kingdom

a.k.k.potrykus@swansea.ac.uk

Received: February 11, 2008
Accepted: August 20, 2008

ABSTRACT

We consider pseudodifferential operators that have non-smooth negative definite symbols and develop a corresponding symbolic calculus. Combining this symbolic calculus with the use of non-smooth symbols that are asymptotically constant in the co-variable we succeed in finding a parametrix for a certain pseudodifferential equation. This in turn allows us to show that some pseudodifferential operators with non-smooth negative definite symbols are pregenerators of Feller semigroups.

Key words: symbolic calculus, non-smooth symbols, negative definite functions, Feller semigroups.
2000 Mathematics Subject Classification:
47D06, 47G30, 35S05, 60J35, 47A53.