Full paper in PDF format:
$%K. P. Evans and N. Jacob, Feller semigroups obtained by variable order subordination, Rev. Mat. Complut. 20 (2007), no. 2, 293–307.%$

Feller Semigroups Obtained by
Variable Order Subordination
Kristian P. EVANS and Niels JACOB
Department of Mathematics
University of Wales Swansea
Singleton Park
Swansea SA2 8PP — United Kingdom

makpe@swan.ac.uk    N.Jacob@swan.ac.uk

Received: August 25, 2006
Accepted: December 18, 2006

ABSTRACT

For certain classes of negative definite symbols q(x,ξ) and state space dependent Bernstein function f(x,s) we prove that -p(x,D), the pseudo-differential operator with symbol -p(x,ξ) = -f(x,q(x,ξ)), extends to the generator of a Feller semigroup. Our result extends previously known results related to operators of variable (fractional) order of differentiation, or variable order fractional powers. New concrete examples are given.

Key words: Feller semigroups, subordination in the sense of Bochner, pseudo-differential operators with negative definite symbols of variable order, Hoh’s symbolic calculus.
2000 Mathematics Subject Classification:
47D07, 47D06, 35S05, 46E35, 60J35.