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