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Keywords:

  • Subordination in the sense of Bochner;
  • pseudo-differential operators of variable order;
  • Feller semigroups;
  • MSC (2010) 47006;
  • 47007;
  • 47G30;
  • 35S05;
  • 60J35

Abstract

For a large class of pseudo-differential operators with a negative definite symbol q(x, ξ) in the sense of Hoh and for a large family of x-dependent Bernstein functions f(x, ·) we prove that the pseudo-differential operator with symbol −f(x, q(x, ξ)) has an extension generating a Feller semigroup. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim