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A symbolic calculus for pseudo differential operators generating Feller semigroups. (English) Zbl 0922.47045
The author introduces a calculus of pseudodifferential operators similar to the classical case of Hörmander classes.
From the text: “Hörmander type symbols are not good choice in general for the operators we have in mind, but anyhow such calculus typically yields estimates in $$L^2$$-context and on the other hand needs no oscillation bounds for the symbols. In this way, it combines in a sense the advantages of both upper approaches”.

MSC:
 47G30 Pseudodifferential operators 35S05 Pseudodifferential operators as generalizations of partial differential operators 58J70 Invariance and symmetry properties for PDEs on manifolds